Gitta Kutyniok - Author Profile

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Kutyniok, Gitta

Author ID:	kutyniok.gitta
Published as:	Kutyniok, Gitta
Homepage:	https://www.ai.math.uni-muenchen.de/members/professor/kutyniok/index.html
External Links:	MGP · ORCID · Wikidata · Google Scholar · ResearchGate · Twitter · dblp · GND · IdRef
Videos:	carmin.tv

Documents Indexed:	122 Publications since 1998, including 2 Books and 10 Additional arXiv Preprints
	20 Contributions as Editor
Co-Authors:	136 Co-Authors with 123 Joint Publications
	4,521 Co-Co-Authors

all top 5

Co-Authors

19	single-authored
17	Casazza, Peter George
16	Lim, Wang-Q
12	Petersen, Philipp Christian
9	Boche, Holger
9	Grohs, Philipp
7	Rauhut, Holger
6	Calderbank, Arthur Robert
6	Labate, Demetrio
5	Heil, Christopher E.
5	Lemvig, Jakob
5	Philipp, Friedrich
5	Strohmer, Thomas
5	Zhuang, Xiaosheng
4	Andrade-Loarca, Hector
4	Dahlke, Stephan
4	Daubechies, Ingrid
4	Keiper, Sandra
4	Levie, Ron
4	Raslan, Mones
4	Speegle, Darrin M.
3	Bacho, Aras
3	Krahmer, Felix
3	März, Maximilian
3	Okoudjou, Kasso A.
3	Öktem, Ozan
3	Schafer, Martin
3	Steidl, Gabriele
2	Berner, Julius
2	Bodmann, Bernhard G.
2	Cahill, Jameson
2	Caire, Giuseppe
2	Czaja, Wojciech
2	Dahmen, Wolfgang A.
2	Flinth, Axel
2	Fono, Adalbert
2	Genzel, Martin
2	Gröchenig, Karlheinz
2	Gühring, Ingo
2	Han, Bin
2	Heinecke, Andreas
2	Jørgensen, Palle E. T.
2	Kittipoom, Pisamai
2	Ma, Jackie
2	Mathar, Rudolf
2	Ólafsson, Gestur
2	Pezeshki, Ali
2	Sauer, Tomas
2	Schneider, Reinhold
2	Scholl, Philipp
2	Schwab, Christoph
2	Shen, Zuowei
2	Silvestrov, Sergei D.
2	Stevenson, Rob P.
2	Teschke, Gerd
2	Vybíral, Jan
2	Welper, Gerrit
1	Adcock, Ben
1	Avron, Haim
1	Balan, Radu V.
1	Bieker, Katharina
1	Bodmann, Bernard G.
1	Bölcskei, Helmut
1	Boufounos, Petros T.
1	Bronstein, Michael M.
1	Bruna, Joan
1	Bubba, Tatiana A.
1	Bucci, Lorenzo
1	Chen, Xuemei
1	Cremers, Daniel
1	de Abreu, Nair Maria Maia
1	Do, Van Tiep
1	Donoho, David Leigh
1	Edidin, Dan
1	Eisert, Jens
1	Geist, Moritz
1	Goeßmann, Alex
1	Götte, Michael
1	Gribonval, Rémi
1	Guo, Kanghui
1	Haber, Eldad
1	Haddadin, Sami
1	Han, Deguang
1	Hansen, Anders C.
1	Hauch, Sascha
1	Hege, Julius
1	Helmberg, Christoph
1	Huang, Chunyan
1	Huang, Wei
1	Jung, Jaesug
1	Kaniuth, Eberhard
1	King, Emily Jeannette
1	Kornelson, Keri A.
1	Kunsch, Robert J.
1	Kussaba, Hugo Tadashi M.
1	Lammers, Mark C.
1	Larson, David Royal
1	Lassas, Matti J.
1	Lee, Dae Gwan
1	Lee, Yunseok
1	Li, Shidong
...and 36 more Co-Authors

all top 5

Serials

14	Applied and Computational Harmonic Analysis
8	Oberwolfach Reports
6	Linear Algebra and its Applications
6	Applied and Numerical Harmonic Analysis
5	IEEE Transactions on Information Theory
5	Constructive Approximation
5	SIAM Journal on Imaging Sciences
4	SIAM Journal on Mathematical Analysis
4	The Journal of Fourier Analysis and Applications
3	Journal of Mathematical Analysis and Applications
3	Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV)
3	Proceedings of the American Mathematical Society
3	Advances in Computational Mathematics
3	GAMM-Mitteilungen
2	Journal of Approximation Theory
2	Journal of Operator Theory
2	The Journal of Geometric Analysis
2	Journal of Mathematical Imaging and Vision
2	Analysis and Applications (Singapore)
1	Communications on Pure and Applied Mathematics
1	Houston Journal of Mathematics
1	Inverse Problems
1	ACM Transactions on Mathematical Software
1	Archiv der Mathematik
1	Colloquium Mathematicum
1	Illinois Journal of Mathematics
1	Journal of Computational and Applied Mathematics
1	Journal of Functional Analysis
1	Numerical Functional Analysis and Optimization
1	SIAM Journal on Numerical Analysis
1	Transactions of the American Mathematical Society
1	Internationale Mathematische Nachrichten
1	Journal of Scientific Computing
1	Computational Statistics
1	Journal of Inverse and Ill-Posed Problems
1	The Journal of Artificial Intelligence Research (JAIR)
1	Foundations of Computational Mathematics
1	Journal of Machine Learning Research (JMLR)
1	Sampling Theory in Signal and Image Processing
1	International Journal of Wavelets, Multiresolution and Information Processing
1	The Journal of Mathematical Sciences. New Series
1	Lecture Notes in Mathematics
1	Operators and Matrices
1	Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
1	SIAM Journal on Mathematics of Data Science

all top 5

Fields

86	Harmonic analysis on Euclidean spaces (42-XX)
62	Information and communication theory, circuits (94-XX)
53	Numerical analysis (65-XX)
34	Computer science (68-XX)
19	General and overarching topics; collections (00-XX)
17	Approximations and expansions (41-XX)
13	Functional analysis (46-XX)
11	Partial differential equations (35-XX)
11	Abstract harmonic analysis (43-XX)
10	Linear and multilinear algebra; matrix theory (15-XX)
8	Operator theory (47-XX)
7	Operations research, mathematical programming (90-XX)
2	Combinatorics (05-XX)
2	Measure and integration (28-XX)
2	Probability theory and stochastic processes (60-XX)
1	Number theory (11-XX)
1	Integral equations (45-XX)
1	Convex and discrete geometry (52-XX)
1	Statistics (62-XX)
1	Statistical mechanics, structure of matter (82-XX)
1	Biology and other natural sciences (92-XX)
1	Systems theory; control (93-XX)

Publications by Year

all cited Publications top 5 cited Publications

Citations contained in zbMATH Open

110 Publications have been cited 2,661 times in 1,398 Documents	Cited by ▼	Year ▼
Frames of subspaces. Zbl 1058.42019 Casazza, Peter G.; Kutyniok, Gitta	233	2004
Fusion frames and distributed processing. Zbl 1258.42029 Casazza, Peter G.; Kutyniok, Gitta; Li, Shidong	182	2008
Finite frames. Theory and applications. Zbl 1257.42001	164	2013
Resolution of the wavefront set using continuous shearlets. Zbl 1169.42012 Kutyniok, Gitta; Labate, Demetrio	110	2009
Sparse multidimensional representations using anisotropic dilation and shear operators. Zbl 1099.65148 Guo, Kanghui; Kutyniok, Gitta; Labate, Demetrio	96	2006
Shearlets. Multiscale analysis for multivariate data. Zbl 1237.42001	94	2012
Optimal approximation with sparsely connected deep neural networks. Zbl 1499.41029 Bölcskei, Helmut; Grohs, Philipp; Kutyniok, Gitta; Petersen, Philipp	94	2019
Shearlet coorbit spaces and associated Banach frames. Zbl 1171.42019 Dahlke, Stephan; Kutyniok, Gitta; Steidl, Gabriele; Teschke, Gerd	85	2009
The uncertainty principle associated with the continuous shearlet transform. Zbl 1257.42047 Dahlke, Stephan; Kutyniok, Gitta; Maass, Peter; Sagiv, Chen; Stark, Hans-Georg; Teschke, Gerd	77	2008
Compactly supported shearlets are optimally sparse. Zbl 1226.42031 Kutyniok, Gitta; Lim, Wang-Q	62	2011
Error bounds for approximations with deep ReLU neural networks in \(W^{s , p}\) norms. Zbl 1452.41009 Gühring, Ingo; Kutyniok, Gitta; Petersen, Philipp	58	2020
A theoretical analysis of deep neural networks and parametric PDEs. Zbl 07493717 Kutyniok, Gitta; Petersen, Philipp; Raslan, Mones; Schneider, Reinhold	56	2022
Construction of compactly supported shearlet frames. Zbl 1239.42031 Kittipoom, Pisamai; Kutyniok, Gitta; Lim, Wang-Q	49	2012
Robust dimension reduction, fusion frames, and Grassmannian packings. Zbl 1283.42046 Kutyniok, Gitta; Pezeshki, Ali; Calderbank, Robert; Liu, Taotao	45	2009
Scalable frames. Zbl 1260.42023 Kutyniok, Gitta; Okoudjou, Kasso A.; Philipp, Friedrich; Tuley, Elizabeth K.	42	2013
Introduction to shearlets. Zbl 1251.42010 Kutyniok, Gitta; Labate, Demetrio	41	2012
Duality principles in frame theory. Zbl 1058.42020 Casazza, Peter G.; Kutyniok, Gitta; Lammers, Mark C.	40	2004
A new identity for Parseval frames. Zbl 1136.42308 Balan, Radu; Casazza, Peter G.; Edidin, Dan; Kutyniok, Gitta	37	2007
Microlocal analysis of the geometric separation problem. Zbl 1261.94007 Donoho, David; Kutyniok, Gitta	37	2013
Zeros of the Zak transform on locally compact Abelian groups. Zbl 0907.43005 Kaniuth, Eberhard; Kutyniok, Gitta	35	1998
Parabolic molecules. Zbl 1403.42038 Grohs, Philipp; Kutyniok, Gitta	35	2014
Robustness of fusion frames under erasures of subspaces and of local frame vectors. Zbl 1256.94017 Casazza, Peter G.; Kutyniok, Gitta	33	2008
Approximation spaces of deep neural networks. Zbl 1491.82017 Gribonval, Rémi; Kutyniok, Gitta; Nielsen, Morten; Voigtlaender, Felix	29	2022
Sparse fusion frames: existence and construction. Zbl 1264.94042 Calderbank, Robert; Casazza, Peter G.; Heinecke, Andreas; Kutyniok, Gitta; Pezeshki, Ali	28	2011
Optimally sparse approximations of 3D functions by compactly supported shearlet frames. Zbl 1252.42043 Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q	28	2012
Learning the invisible: a hybrid deep learning-shearlet framework for limited angle computed tomography. Zbl 1416.92099 Bubba, Tatiana A.; Kutyniok, Gitta; Lassas, Matti; März, Maximilian; Samek, Wojciech; Siltanen, Samuli; Srinivasan, Vignesh	27	2019
Numerical solution of the parametric diffusion equation by deep neural networks. Zbl 1473.35331 Geist, Moritz; Petersen, Philipp; Raslan, Mones; Schneider, Reinhold; Kutyniok, Gitta	26	2021
ShearLab 3D: faithful digital shearlet transforms based on compactly supported shearlets. Zbl 1347.65203 Kutyniok, Gitta; Lim, Wang-Q; Reisenhofer, Rafael	26	2016
Density of weighted wavelet frames. Zbl 1029.42031 Heil, Christopher; Kutyniok, Gitta	25	2003
Analysis of inpainting via clustered sparsity and microlocal analysis. Zbl 1362.94007 King, Emily J.; Kutyniok, Gitta; Zhuang, Xiaosheng	24	2014
Introduction to finite frame theory. Zbl 1281.42032 Casazza, Peter G.; Kutyniok, Gitta; Philipp, Friedrich	23	2013
Classification of edges using compactly supported shearlets. Zbl 1378.42023 Kutyniok, Gitta; Petersen, Philipp	23	2017
Optimally sparse frames. Zbl 1365.94059 Casazza, Peter G.; Heinecke, Andreas; Krahmer, Felix; Kutyniok, Gitta	23	2011
ShearLab: a rational design of a digital parabolic scaling algorithm. Zbl 1257.42048 Kutyniok, Gitta; Shahram, Morteza; Zhuang, Xiaosheng	22	2012
The Balian-Low theorem for symplectic lattices in higher dimensions. Zbl 1017.42027 Gröchenig, Karlheinz; Han, Deguang; Heil, Christopher; Kutyniok, Gitta	22	2002
The geometry of sets of parameters of wave packet frames. Zbl 1095.42020 Czaja, Wojciech; Kutyniok, Gitta; Speegle, Darrin	22	2006
Sparse recovery from combined fusion frame measurements. Zbl 1365.94066 Boufounos, Petros; Kutyniok, Gitta; Rauhut, Holger	21	2011
The theory of reproducing systems on locally compact abelian groups. Zbl 1113.43008 Kutyniok, Gitta; Labate, Demetrio	20	2006
Adaptive directional subdivision schemes and shearlet multiresolution analysis. Zbl 1193.42127 Kutyniok, Gitta; Sauer, Tomas	20	2009
Affine density in wavelet analysis. Zbl 1142.42017 Kutyniok, Gitta	19	2007
Adaptive multiresolution analysis structures and shearlet systems. Zbl 1283.42053 Han, Bin; Kutyniok, Gitta; Shen, Zuowei	17	2011
Theory and applications of compressed sensing. Zbl 1283.94018 Kutyniok, Gitta	16	2013
Linear stable sampling rate: optimality of 2D wavelet reconstructions from Fourier measurements. Zbl 1331.42036 Adcock, Ben; Hansen, Anders C.; Kutyniok, Gitta; Ma, Jackie	16	2015
The homogeneous approximation property for wavelet frames. Zbl 1133.42049 Heil, Christopher; Kutyniok, Gitta	16	2007
Landau’s necessary density conditions for LCA groups. Zbl 1158.43004 Gröchenig, Karlheinz; Kutyniok, Gitta; Seip, Kristian	16	2008
A quantitative notion of redundancy for finite frames. Zbl 1211.42027 Bodmann, Bernhard G.; Casazza, Peter G.; Kutyniok, Gitta	15	2011
\(\alpha\)-Molecules. Zbl 1342.42041 Grohs, Philipp; Keiper, Sandra; Kutyniok, Gitta; Schäfer, Martin	15	2016
Beurling dimension of Gabor pseudoframes for affine subspaces. Zbl 1268.42055 Czaja, Wojciech; Kutyniok, Gitta; Speegle, Darrin	14	2008
Asymptotic analysis of inpainting via universal shearlet systems. Zbl 1307.42033 Genzel, Martin; Kutyniok, Gitta	13	2014
Compactly supported shearlets. Zbl 1252.42042 Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q	13	2012
The modern mathematics of deep learning. (Die moderne Mathematik des tiefen Lernens.) Zbl 07571594 Berner, Julius; Grohs, Philipp; Kutyniok, Gitta; Petersen, Philipp	13	2021
A survey of compressed sensing. Zbl 1333.94015 Boche, Holger; Calderbank, Robert; Kutyniok, Gitta; Vybíral, Jan	13	2015
Sparsity and spectral properties of dual frames. Zbl 1280.42026 Krahmer, Felix; Kutyniok, Gitta; Lemvig, Jakob	12	2013
Image separation using wavelets and shearlets. Zbl 1345.94007 Kutyniok, Gitta; Lim, Wang-Q	12	2012
A generalization of Gram-Schmidt orthogonalization generating all Parseval frames. Zbl 1118.65027 Casazza, Peter G.; Kutyniok, Gitta	12	2007
Wilson bases for general time-frequency lattices. Zbl 1090.94008 Kutyniok, Gitta; Strohmer, Thomas	12	2005
Fusion frames. Zbl 1261.42048 Casazza, Peter G.; Kutyniok, Gitta	12	2013
Scalable frames and convex geometry. Zbl 1307.42029 Kutyniok, Gitta; Okoudjou, Kasso A.; Philipp, Friedrich	11	2014
Extraction of digital wavefront sets using applied harmonic analysis and deep neural networks. Zbl 1439.35009 Andrade-Loarca, Hector; Kutyniok, Gitta; Öktem, Ozan; Petersen, Philipp C.	11	2019
Gabor shearlets. Zbl 1304.42084 Bodmann, Bernhard G.; Kutyniok, Gitta; Zhuang, Xiaosheng	10	2015
Geometric separation by single-pass alternating thresholding. Zbl 1357.42033 Kutyniok, Gitta	10	2014
Cartoon approximation with \(\alpha\)-curvelets. Zbl 1359.42018 Grohs, Philipp; Keiper, Sandra; Kutyniok, Gitta; Schäfer, Martin	10	2016
Optimal compressive imaging of Fourier data. Zbl 1437.94043 Kutyniok, Gitta; Lim, Wang-Q	10	2018
Affine density, frame bounds, and the admissibility condition for wavelet frames. Zbl 1124.42027 Kutyniok, Gitta	9	2007
Digital shearlet transforms. Zbl 1255.94021 Kutyniok, Gitta; Lim, Wang-Q; Zhuang, Xiaosheng	9	2012
Linear independence of time-frequency shifts under a generalized Schrödinger representation. Zbl 0997.43006 Kutyniok, Gitta	9	2002
A qualitative uncertainty principle for functions generating a Gabor frame on LCA groups. Zbl 1023.43003 Kutyniok, Gitta	9	2003
Measures of scalability. Zbl 1359.94307 Chen, Xuemei; Kutyniok, Gitta; Okoudjou, Kasso A.; Philipp, Friedrich; Wang, Rongrong	9	2015
Compressed sensing for finite-valued signals. Zbl 1370.94153 Keiper, Sandra; Kutyniok, Gitta; Lee, Dae Gwan; Pfander, Götz E.	9	2017
The computational complexity of understanding binary classifier decisions. Zbl 1512.68116 Wäldchen, Stephan; Macdonald, Jan; Hauch, Sascha; Kutyniok, Gitta	9	2021
Operators and frames. Zbl 1289.42088 Cahill, Jameson; Casazza, Peter G.; Kutyniok, Gitta	8	2013
PROMP: a sparse recovery approach to lattice-valued signals. Zbl 1408.94862 Flinth, Axel; Kutyniok, Gitta	8	2018
\(\ell^1\)-analysis minimization and generalized (co-)sparsity: when does recovery succeed? Zbl 1460.94021 Genzel, Martin; Kutyniok, Gitta; März, Maximilian	8	2021
Efficient resolution of anisotropic structures. Zbl 1317.65251 Dahmen, Wolfgang; Huang, Chunyan; Kutyniok, Gitta; Lim, Wang-Q; Schwab, Christoph; Welper, Gerrit	7	2014
Irregular shearlet frames: Geometry and approximation properties. Zbl 1226.42030 Kittipoom, Pisamai; Kutyniok, Gitta; Lim, Wang-Q	7	2011
Time-frequency analysis on locally compact groups. Zbl 0971.43001 Kutyniok, Gitta	7	2000
Ambiguity functions, Wigner distributions and Cohen’s class for LCA groups. Zbl 1032.43002 Kutyniok, Gitta	7	2003
The Zak transform on certain locally compact groups. Zbl 1079.43009 Kutyniok, Gitta	7	2002
The effect of perturbations of operator-valued frame sequences and fusion frames on their duals. Zbl 1383.42031 Kutyniok, Gitta; Paternostro, Victoria; Philipp, Friedrich	7	2017
A decomposition theorem for frames and the Feichtinger conjecture. Zbl 1155.46010 Casazza, Peter G.; Kutyniok, Gitta; Speegle, Darrin; Tremain, Janet C.	6	2008
Clustered sparsity and separation of cartoon and texture. Zbl 1280.42036 Kutyniok, Gitta	6	2013
A weak qualitative uncertainty principle for compact groups. Zbl 1031.43003 Kutyniok, Gitta	6	2003
Adaptive anisotropic Petrov-Galerkin methods for first order transport equations. Zbl 1435.65197 Dahmen, Wolfgang; Kutyniok, Gitta; Lim, Wang-Q; Schwab, Christoph; Welper, Gerrit	6	2018
Density of frames and Schauder bases of windowed exponentials. Zbl 1214.42070 Heil, Christopher; Kutyniok, Gitta	5	2008
A redundant version of the Rado-Horn theorem. Zbl 1103.15001 Casazza, Peter G.; Kutyniok, Gitta; Speegle, Darrin	5	2006
Shearlets and optimally sparse approximations. Zbl 1251.42008 Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q	5	2012
The modern mathematics of deep learning. Zbl 1520.68165 Berner, Julius; Grohs, Philipp; Kutyniok, Gitta; Petersen, Philipp	5	2023
Expressivity of deep neural networks. Zbl 1523.68080 Gühring, Ingo; Raslan, Mones; Kutyniok, Gitta	5	2023
Parabolic molecules: Curvelets, shearlets, and beyond. Zbl 1331.42038 Grohs, Philipp; Keiper, Sandra; Kutyniok, Gitta; Schäfer, Martin	4	2014
From wavelets to shearlets and back again. Zbl 1227.65139 Kutyniok, Gitta; Sauer, Tomas	4	2008
Compressed sensing and its applications. MATHEON workshop, Berlin, Germany, December 2013. Zbl 1320.94007	4	2015
Beurling density and shift-invariant weighted irregular Gabor systems. Zbl 1156.42311 Kutyniok, Gitta	4	2006
Shearlets on bounded domains. Zbl 1253.42035 Kutyniok, Gitta; Lim, Wang-Q	3	2012
The local integrability condition for wavelet frames. Zbl 1101.42018 Kutyniok, Gitta	3	2006
Shearlets: theory and applications. Zbl 1311.42091 Kutyniok, Gitta; Lim, Wang-Q; Steidl, Gabriele	3	2014
Compressed sensing and its applications. Selected papers of the third international MATHEON conference, TU Berlin, Berlin, Germany, December 4–8, 2017. Zbl 1427.94002	3	2019
Regularization and numerical solution of the inverse scattering problem using shearlet frames. Zbl 1365.65244 Kutyniok, Gitta; Mehrmann, Volker; Petersen, Philipp C.	3	2017
Dualizable shearlet frames and sparse approximation. Zbl 1366.65119 Kutyniok, Gitta; Lim, Wang-Q	3	2016
Mini-workshop: Shearlets. Abstracts from the mini-workshop held October 3rd – October 9th, 2010. Zbl 1235.00037	2	2010
Analysis of simultaneous inpainting and geometric separation based on sparse decomposition. Zbl 07528664 Do, Van Tiep; Levie, Ron; Kutyniok, Gitta	2	2022
The modern mathematics of deep learning. Zbl 1520.68165 Berner, Julius; Grohs, Philipp; Kutyniok, Gitta; Petersen, Philipp	5	2023
Expressivity of deep neural networks. Zbl 1523.68080 Gühring, Ingo; Raslan, Mones; Kutyniok, Gitta	5	2023
Limitations of deep learning for inverse problems on digital hardware. Zbl 07884100 Boche, Holger; Fono, Adalbert; Kutyniok, Gitta	1	2023
The mathematics of artificial intelligence. Zbl 1535.68295 Kutyniok, Gitta	1	2023
A theoretical analysis of deep neural networks and parametric PDEs. Zbl 07493717 Kutyniok, Gitta; Petersen, Philipp; Raslan, Mones; Schneider, Reinhold	56	2022
Approximation spaces of deep neural networks. Zbl 1491.82017 Gribonval, Rémi; Kutyniok, Gitta; Nielsen, Morten; Voigtlaender, Felix	29	2022
Analysis of simultaneous inpainting and geometric separation based on sparse decomposition. Zbl 07528664 Do, Van Tiep; Levie, Ron; Kutyniok, Gitta	2	2022
Deep microlocal reconstruction for limited-angle tomography. Zbl 07522506 Andrade-Loarca, Héctor; Kutyniok, Gitta; Öktem, Ozan; Petersen, Philipp	2	2022
Numerical solution of the parametric diffusion equation by deep neural networks. Zbl 1473.35331 Geist, Moritz; Petersen, Philipp; Raslan, Mones; Schneider, Reinhold; Kutyniok, Gitta	26	2021
The modern mathematics of deep learning. (Die moderne Mathematik des tiefen Lernens.) Zbl 07571594 Berner, Julius; Grohs, Philipp; Kutyniok, Gitta; Petersen, Philipp	13	2021
The computational complexity of understanding binary classifier decisions. Zbl 1512.68116 Wäldchen, Stephan; Macdonald, Jan; Hauch, Sascha; Kutyniok, Gitta	9	2021
\(\ell^1\)-analysis minimization and generalized (co-)sparsity: when does recovery succeed? Zbl 1460.94021 Genzel, Martin; Kutyniok, Gitta; März, Maximilian	8	2021
Transferability of spectral graph convolutional neural networks. Zbl 1539.68305 Levie, Ron; Huang, Wei; Bucci, Lorenzo; Bronstein, Michael; Kutyniok, Gitta	2	2021
Error bounds for approximations with deep ReLU neural networks in \(W^{s , p}\) norms. Zbl 1452.41009 Gühring, Ingo; Kutyniok, Gitta; Petersen, Philipp	58	2020
Shearlets as feature extractor for semantic edge detection: the model-based and data-driven realm. Zbl 1472.94004 Andrade-Loarca, Héctor; Kutyniok, Gitta; Öktem, Ozan	2	2020
Anisotropic multiscale systems on bounded domains. Zbl 1442.42076 Grohs, Philipp; Kutyniok, Gitta; Ma, Jackie; Petersen, Philipp; Raslan, Mones	1	2020
Optimal approximation with sparsely connected deep neural networks. Zbl 1499.41029 Bölcskei, Helmut; Grohs, Philipp; Kutyniok, Gitta; Petersen, Philipp	94	2019
Learning the invisible: a hybrid deep learning-shearlet framework for limited angle computed tomography. Zbl 1416.92099 Bubba, Tatiana A.; Kutyniok, Gitta; Lassas, Matti; März, Maximilian; Samek, Wojciech; Siltanen, Samuli; Srinivasan, Vignesh	27	2019
Extraction of digital wavefront sets using applied harmonic analysis and deep neural networks. Zbl 1439.35009 Andrade-Loarca, Hector; Kutyniok, Gitta; Öktem, Ozan; Petersen, Philipp C.	11	2019
Compressed sensing and its applications. Selected papers of the third international MATHEON conference, TU Berlin, Berlin, Germany, December 4–8, 2017. Zbl 1427.94002	3	2019
Optimal compressive imaging of Fourier data. Zbl 1437.94043 Kutyniok, Gitta; Lim, Wang-Q	10	2018
PROMP: a sparse recovery approach to lattice-valued signals. Zbl 1408.94862 Flinth, Axel; Kutyniok, Gitta	8	2018
Adaptive anisotropic Petrov-Galerkin methods for first order transport equations. Zbl 1435.65197 Dahmen, Wolfgang; Kutyniok, Gitta; Lim, Wang-Q; Schwab, Christoph; Welper, Gerrit	6	2018
Classification of edges using compactly supported shearlets. Zbl 1378.42023 Kutyniok, Gitta; Petersen, Philipp	23	2017
Compressed sensing for finite-valued signals. Zbl 1370.94153 Keiper, Sandra; Kutyniok, Gitta; Lee, Dae Gwan; Pfander, Götz E.	9	2017
The effect of perturbations of operator-valued frame sequences and fusion frames on their duals. Zbl 1383.42031 Kutyniok, Gitta; Paternostro, Victoria; Philipp, Friedrich	7	2017
Regularization and numerical solution of the inverse scattering problem using shearlet frames. Zbl 1365.65244 Kutyniok, Gitta; Mehrmann, Volker; Petersen, Philipp C.	3	2017
Compressed sensing and its applications. Second international MATHEON conference, December 2015. Zbl 1388.94005	1	2017
ShearLab 3D: faithful digital shearlet transforms based on compactly supported shearlets. Zbl 1347.65203 Kutyniok, Gitta; Lim, Wang-Q; Reisenhofer, Rafael	26	2016
\(\alpha\)-Molecules. Zbl 1342.42041 Grohs, Philipp; Keiper, Sandra; Kutyniok, Gitta; Schäfer, Martin	15	2016
Cartoon approximation with \(\alpha\)-curvelets. Zbl 1359.42018 Grohs, Philipp; Keiper, Sandra; Kutyniok, Gitta; Schäfer, Martin	10	2016
Dualizable shearlet frames and sparse approximation. Zbl 1366.65119 Kutyniok, Gitta; Lim, Wang-Q	3	2016
Linear stable sampling rate: optimality of 2D wavelet reconstructions from Fourier measurements. Zbl 1331.42036 Adcock, Ben; Hansen, Anders C.; Kutyniok, Gitta; Ma, Jackie	16	2015
A survey of compressed sensing. Zbl 1333.94015 Boche, Holger; Calderbank, Robert; Kutyniok, Gitta; Vybíral, Jan	13	2015
Gabor shearlets. Zbl 1304.42084 Bodmann, Bernhard G.; Kutyniok, Gitta; Zhuang, Xiaosheng	10	2015
Measures of scalability. Zbl 1359.94307 Chen, Xuemei; Kutyniok, Gitta; Okoudjou, Kasso A.; Philipp, Friedrich; Wang, Rongrong	9	2015
Compressed sensing and its applications. MATHEON workshop, Berlin, Germany, December 2013. Zbl 1320.94007	4	2015
Parabolic molecules. Zbl 1403.42038 Grohs, Philipp; Kutyniok, Gitta	35	2014
Analysis of inpainting via clustered sparsity and microlocal analysis. Zbl 1362.94007 King, Emily J.; Kutyniok, Gitta; Zhuang, Xiaosheng	24	2014
Asymptotic analysis of inpainting via universal shearlet systems. Zbl 1307.42033 Genzel, Martin; Kutyniok, Gitta	13	2014
Scalable frames and convex geometry. Zbl 1307.42029 Kutyniok, Gitta; Okoudjou, Kasso A.; Philipp, Friedrich	11	2014
Geometric separation by single-pass alternating thresholding. Zbl 1357.42033 Kutyniok, Gitta	10	2014
Efficient resolution of anisotropic structures. Zbl 1317.65251 Dahmen, Wolfgang; Huang, Chunyan; Kutyniok, Gitta; Lim, Wang-Q; Schwab, Christoph; Welper, Gerrit	7	2014
Parabolic molecules: Curvelets, shearlets, and beyond. Zbl 1331.42038 Grohs, Philipp; Keiper, Sandra; Kutyniok, Gitta; Schäfer, Martin	4	2014
Shearlets: theory and applications. Zbl 1311.42091 Kutyniok, Gitta; Lim, Wang-Q; Steidl, Gabriele	3	2014
Sparse matrices in frame theory. Zbl 1306.65082 Krahmer, Felix; Kutyniok, Gitta; Lemvig, Jakob	1	2014
Compressed sensing. Zbl 1336.94022 Kutyniok, Gitta	1	2014
Finite frames. Theory and applications. Zbl 1257.42001	164	2013
Scalable frames. Zbl 1260.42023 Kutyniok, Gitta; Okoudjou, Kasso A.; Philipp, Friedrich; Tuley, Elizabeth K.	42	2013
Microlocal analysis of the geometric separation problem. Zbl 1261.94007 Donoho, David; Kutyniok, Gitta	37	2013
Introduction to finite frame theory. Zbl 1281.42032 Casazza, Peter G.; Kutyniok, Gitta; Philipp, Friedrich	23	2013
Theory and applications of compressed sensing. Zbl 1283.94018 Kutyniok, Gitta	16	2013
Sparsity and spectral properties of dual frames. Zbl 1280.42026 Krahmer, Felix; Kutyniok, Gitta; Lemvig, Jakob	12	2013
Fusion frames. Zbl 1261.42048 Casazza, Peter G.; Kutyniok, Gitta	12	2013
Operators and frames. Zbl 1289.42088 Cahill, Jameson; Casazza, Peter G.; Kutyniok, Gitta	8	2013
Clustered sparsity and separation of cartoon and texture. Zbl 1280.42036 Kutyniok, Gitta	6	2013
Shearlets. Multiscale analysis for multivariate data. Zbl 1237.42001	94	2012
Construction of compactly supported shearlet frames. Zbl 1239.42031 Kittipoom, Pisamai; Kutyniok, Gitta; Lim, Wang-Q	49	2012
Introduction to shearlets. Zbl 1251.42010 Kutyniok, Gitta; Labate, Demetrio	41	2012
Optimally sparse approximations of 3D functions by compactly supported shearlet frames. Zbl 1252.42043 Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q	28	2012
ShearLab: a rational design of a digital parabolic scaling algorithm. Zbl 1257.42048 Kutyniok, Gitta; Shahram, Morteza; Zhuang, Xiaosheng	22	2012
Compactly supported shearlets. Zbl 1252.42042 Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q	13	2012
Image separation using wavelets and shearlets. Zbl 1345.94007 Kutyniok, Gitta; Lim, Wang-Q	12	2012
Digital shearlet transforms. Zbl 1255.94021 Kutyniok, Gitta; Lim, Wang-Q; Zhuang, Xiaosheng	9	2012
Shearlets and optimally sparse approximations. Zbl 1251.42008 Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q	5	2012
Shearlets on bounded domains. Zbl 1253.42035 Kutyniok, Gitta; Lim, Wang-Q	3	2012
Compactly supported shearlets are optimally sparse. Zbl 1226.42031 Kutyniok, Gitta; Lim, Wang-Q	62	2011
Sparse fusion frames: existence and construction. Zbl 1264.94042 Calderbank, Robert; Casazza, Peter G.; Heinecke, Andreas; Kutyniok, Gitta; Pezeshki, Ali	28	2011
Optimally sparse frames. Zbl 1365.94059 Casazza, Peter G.; Heinecke, Andreas; Krahmer, Felix; Kutyniok, Gitta	23	2011
Sparse recovery from combined fusion frame measurements. Zbl 1365.94066 Boufounos, Petros; Kutyniok, Gitta; Rauhut, Holger	21	2011
Adaptive multiresolution analysis structures and shearlet systems. Zbl 1283.42053 Han, Bin; Kutyniok, Gitta; Shen, Zuowei	17	2011
A quantitative notion of redundancy for finite frames. Zbl 1211.42027 Bodmann, Bernhard G.; Casazza, Peter G.; Kutyniok, Gitta	15	2011
Irregular shearlet frames: Geometry and approximation properties. Zbl 1226.42030 Kittipoom, Pisamai; Kutyniok, Gitta; Lim, Wang-Q	7	2011
Mini-workshop: Shearlets. Abstracts from the mini-workshop held October 3rd – October 9th, 2010. Zbl 1235.00037	2	2010
Resolution of the wavefront set using continuous shearlets. Zbl 1169.42012 Kutyniok, Gitta; Labate, Demetrio	110	2009
Shearlet coorbit spaces and associated Banach frames. Zbl 1171.42019 Dahlke, Stephan; Kutyniok, Gitta; Steidl, Gabriele; Teschke, Gerd	85	2009
Robust dimension reduction, fusion frames, and Grassmannian packings. Zbl 1283.42046 Kutyniok, Gitta; Pezeshki, Ali; Calderbank, Robert; Liu, Taotao	45	2009
Adaptive directional subdivision schemes and shearlet multiresolution analysis. Zbl 1193.42127 Kutyniok, Gitta; Sauer, Tomas	20	2009
Fusion frames and distributed processing. Zbl 1258.42029 Casazza, Peter G.; Kutyniok, Gitta; Li, Shidong	182	2008
The uncertainty principle associated with the continuous shearlet transform. Zbl 1257.42047 Dahlke, Stephan; Kutyniok, Gitta; Maass, Peter; Sagiv, Chen; Stark, Hans-Georg; Teschke, Gerd	77	2008
Robustness of fusion frames under erasures of subspaces and of local frame vectors. Zbl 1256.94017 Casazza, Peter G.; Kutyniok, Gitta	33	2008
Landau’s necessary density conditions for LCA groups. Zbl 1158.43004 Gröchenig, Karlheinz; Kutyniok, Gitta; Seip, Kristian	16	2008
Beurling dimension of Gabor pseudoframes for affine subspaces. Zbl 1268.42055 Czaja, Wojciech; Kutyniok, Gitta; Speegle, Darrin	14	2008
A decomposition theorem for frames and the Feichtinger conjecture. Zbl 1155.46010 Casazza, Peter G.; Kutyniok, Gitta; Speegle, Darrin; Tremain, Janet C.	6	2008
Density of frames and Schauder bases of windowed exponentials. Zbl 1214.42070 Heil, Christopher; Kutyniok, Gitta	5	2008
From wavelets to shearlets and back again. Zbl 1227.65139 Kutyniok, Gitta; Sauer, Tomas	4	2008
Convolution and Wiener amalgam spaces on the affine group. Zbl 1161.43004 Heil, Christopher; Kutyniok, Gitta	1	2008
A new identity for Parseval frames. Zbl 1136.42308 Balan, Radu; Casazza, Peter G.; Edidin, Dan; Kutyniok, Gitta	37	2007
Affine density in wavelet analysis. Zbl 1142.42017 Kutyniok, Gitta	19	2007
The homogeneous approximation property for wavelet frames. Zbl 1133.42049 Heil, Christopher; Kutyniok, Gitta	16	2007
A generalization of Gram-Schmidt orthogonalization generating all Parseval frames. Zbl 1118.65027 Casazza, Peter G.; Kutyniok, Gitta	12	2007
Affine density, frame bounds, and the admissibility condition for wavelet frames. Zbl 1124.42027 Kutyniok, Gitta	9	2007
Sparse multidimensional representations using anisotropic dilation and shear operators. Zbl 1099.65148 Guo, Kanghui; Kutyniok, Gitta; Labate, Demetrio	96	2006
The geometry of sets of parameters of wave packet frames. Zbl 1095.42020 Czaja, Wojciech; Kutyniok, Gitta; Speegle, Darrin	22	2006
The theory of reproducing systems on locally compact abelian groups. Zbl 1113.43008 Kutyniok, Gitta; Labate, Demetrio	20	2006
A redundant version of the Rado-Horn theorem. Zbl 1103.15001 Casazza, Peter G.; Kutyniok, Gitta; Speegle, Darrin	5	2006
Beurling density and shift-invariant weighted irregular Gabor systems. Zbl 1156.42311 Kutyniok, Gitta	4	2006
The local integrability condition for wavelet frames. Zbl 1101.42018 Kutyniok, Gitta	3	2006
Wilson bases for general time-frequency lattices. Zbl 1090.94008 Kutyniok, Gitta; Strohmer, Thomas	12	2005
Frames of subspaces. Zbl 1058.42019 Casazza, Peter G.; Kutyniok, Gitta	233	2004
...and 10 more Documents

all cited Publications top 5 cited Publications

all top 5

Cited by 1,712 Authors

57	Kutyniok, Gitta
39	Casazza, Peter George
33	Grohs, Philipp
27	Labate, Demetrio
25	Arefijamaal, Ali Akbar
23	Petersen, Philipp Christian
20	Leng, Jinsong
20	Sun, Wenchang
18	Kamyabi-Gol, Rajab Ali
18	Voigtlaender, Felix
17	Vashisht, Lalit Kumar
16	Rahimi, Asghar
15	Bodmann, Bernhard G.
15	Guo, Kanghui
15	Han, Deguang
14	Führ, Hartmut
14	Okoudjou, Kasso A.
13	Adcock, Ben
13	Mixon, Dustin G.
13	Schwab, Christoph
13	Shah, Firdous Ahmad
13	Xiao, Xiangchun
13	Zhu, Yucan
12	Balazs, Peter
12	De Vito, Ernesto
12	Fickus, Matthew C.
12	Hansen, Anders C.
12	Jentzen, Arnulf
12	Steidl, Gabriele
12	Zhuang, Xiaosheng
11	Christensen, Ole
11	Dahlke, Stephan
11	Li, Dongwei
11	Lim, Wang-Q
11	Massey, Pedro G.
11	Stojanoff, Demetrio
10	Ahmadi, Reza H.
10	Aldroubi, Akram
10	Cabrelli, Carlos A.
10	Kaushik, Shiv Kumar
10	Teschke, Gerd
10	Xiang, Zhongqi
9	Asgari, Mohammad Sadegh
9	De Mari, Filippo
9	Deepshikha
9	Feichtinger, Hans Georg
9	Jørgensen, Palle E. T.
9	Lemvig, Jakob
9	Powell, Alexander M.
9	Rahimlou, Gholamreza
9	Ruiz, Mariano A.
9	Shamsabadi, Mitra
8	Czaja, Wojciech
8	Farashahi, Arash Ghaani
8	Gabardo, Jean-Pierre
8	Han, Bin
8	Jyoti
8	Khosravi, Amir
8	Li, Pengtong
8	Pfander, Götz E.
8	Sadri, Vahid
8	Schönlieb, Carola-Bibiane
8	Speegle, Darrin M.
7	Bubba, Tatiana A.
7	Chen, Xuemei
7	Gröchenig, Karlheinz
7	Huang, Ting-Zhu
7	Jakobsen, Mads Sielemann
7	Javanshiri, Hossein
7	King, Emily Jeannette
7	Luef, Franz
7	Mirzaee Azandaryani, Morteza
7	Mishra, Siddhartha
7	Neyshaburi, Fahimeh Arabyani
7	Shen, Zuowei
7	Sun, Qiyu
7	Tantary, Azhar Y.
7	Raisi Tousi, Reihaneh
7	Vera, Daniel J.
6	Alberti, Giovanni S.
6	Benedetto, John Joseph
6	Dehghan, Mohammad Ali
6	Haas, John I. IV
6	Häuser, Sören
6	Heil, Christopher E.
6	Jasper, John Sahayam
6	Krahmer, Felix
6	Larson, David Royal
6	Levie, Ron
6	Li, Yunzhang
6	Maass, Peter
6	Manzoni, Andrea
6	Öktem, Ozan
6	Raslan, Mones
6	Rauhut, Holger
6	Tran, Tin T.
6	Tremain, Janet C.
6	Waldron, Shayne F. D.
6	Wang, Yang
6	Xu, Yuxiang
...and 1,612 more Authors

all top 5

Cited in 293 Serials

125	Applied and Computational Harmonic Analysis
70	The Journal of Fourier Analysis and Applications
57	International Journal of Wavelets, Multiresolution and Information Processing
50	Journal of Mathematical Analysis and Applications
40	Linear Algebra and its Applications
40	Advances in Computational Mathematics
26	Journal of Pseudo-Differential Operators and Applications
21	Journal of Functional Analysis
21	SIAM Journal on Imaging Sciences
20	Numerical Functional Analysis and Optimization
20	Results in Mathematics
18	Constructive Approximation
17	Inverse Problems
17	Analysis and Applications (Singapore)
17	Sahand Communications in Mathematical Analysis
16	Journal of Approximation Theory
15	Linear and Multilinear Algebra
15	Neural Networks
15	Mediterranean Journal of Mathematics
14	Proceedings of the American Mathematical Society
13	SIAM Journal on Scientific Computing
12	Journal of Inequalities and Applications
11	Journal of Computational and Applied Mathematics
11	Foundations of Computational Mathematics
10	Acta Applicandae Mathematicae
10	Bulletin of the Malaysian Mathematical Sciences Society. Second Series
10	Complex Analysis and Operator Theory
9	Journal of Mathematical Physics
9	Journal of Scientific Computing
9	The Journal of Geometric Analysis
9	SIAM Journal on Mathematical Analysis
9	Acta Mathematica Sinica. English Series
9	Sampling Theory, Signal Processing, and Data Analysis
8	Computers & Mathematics with Applications
8	Applied Mathematics and Computation
8	Transactions of the American Mathematical Society
8	Proceedings of the Indian Academy of Sciences. Mathematical Sciences
8	Journal of Mathematical Imaging and Vision
8	Annals of Functional Analysis
7	Applicable Analysis
7	Journal of Computational Physics
7	Rocky Mountain Journal of Mathematics
7	Advances in Mathematics
7	Mathematische Nachrichten
7	SIAM Journal on Mathematics of Data Science
6	Mathematics of Computation
6	Monatshefte für Mathematik
6	Bulletin of the Iranian Mathematical Society
6	Acta Numerica
6	Oberwolfach Reports
6	Science China. Mathematics
5	Computer Methods in Applied Mechanics and Engineering
5	Mathematical Methods in the Applied Sciences
5	Journal of Complexity
5	Advances in Applied Clifford Algebras
5	Sampling Theory in Signal and Image Processing
5	Journal of Physics A: Mathematical and Theoretical
5	Communications in Computational Physics
5	Operators and Matrices
5	Journal of Mathematical Inequalities
5	Palestine Journal of Mathematics
4	Indian Journal of Pure & Applied Mathematics
4	Collectanea Mathematica
4	Mathematics and Computers in Simulation
4	Memoirs of the American Mathematical Society
4	SIAM Journal on Numerical Analysis
4	Circuits, Systems, and Signal Processing
4	Applied Mathematics Letters
4	SIAM Review
4	Integral Transforms and Special Functions
4	Abstract and Applied Analysis
4	Journal of Machine Learning Research (JMLR)
4	Inverse Problems and Imaging
4	Analysis and Mathematical Physics
4	Problemy Analiza. Issues of Analysis
4	Journal of Mathematics
4	SIAM/ASA Journal on Uncertainty Quantification
4	Journal of Linear and Topological Algebra
4	Wavelets and Linear Algebra
4	Korean Journal of Mathematics
3	The Annals of Statistics
3	Advances in Applied Mathematics
3	Multidimensional Systems and Signal Processing
3	Journal de Mathématiques Pures et Appliquées. Neuvième Série
3	Expositiones Mathematicae
3	Georgian Mathematical Journal
3	Opuscula Mathematica
3	Mathematical Problems in Engineering
3	Infinite Dimensional Analysis, Quantum Probability and Related Topics
3	GAMM-Mitteilungen
3	Banach Journal of Mathematical Analysis
3	Asian-European Journal of Mathematics
3	Advances in Pure and Applied Mathematics
3	International Journal of Nonlinear Analysis and Applications
3	Journal of Function Spaces
3	Research in the Mathematical Sciences
3	Advances in Operator Theory
3	Mathematics in Engineering
3	Mathematical Foundations of Computing
3	SN Partial Differential Equations and Applications
...and 193 more Serials

all top 5

Cited in 56 Fields

920	Harmonic analysis on Euclidean spaces (42-XX)
314	Numerical analysis (65-XX)
276	Information and communication theory, circuits (94-XX)
275	Functional analysis (46-XX)
255	Computer science (68-XX)
176	Approximations and expansions (41-XX)
139	Operator theory (47-XX)
95	Abstract harmonic analysis (43-XX)
77	Partial differential equations (35-XX)
69	Linear and multilinear algebra; matrix theory (15-XX)
62	Statistics (62-XX)
47	Topological groups, Lie groups (22-XX)
45	Operations research, mathematical programming (90-XX)
39	Biology and other natural sciences (92-XX)
33	Integral transforms, operational calculus (44-XX)
32	Quantum theory (81-XX)
30	Combinatorics (05-XX)
30	Probability theory and stochastic processes (60-XX)
21	Convex and discrete geometry (52-XX)
20	Number theory (11-XX)
16	Group theory and generalizations (20-XX)
16	Measure and integration (28-XX)
16	Calculus of variations and optimal control; optimization (49-XX)
14	Real functions (26-XX)
13	Fluid mechanics (76-XX)
13	Systems theory; control (93-XX)
10	Functions of a complex variable (30-XX)
10	Global analysis, analysis on manifolds (58-XX)
10	Game theory, economics, finance, and other social and behavioral sciences (91-XX)
8	General and overarching topics; collections (00-XX)
8	Mechanics of deformable solids (74-XX)
7	Special functions (33-XX)
7	Dynamical systems and ergodic theory (37-XX)
7	Geometry (51-XX)
6	Order, lattices, ordered algebraic structures (06-XX)
6	Algebraic geometry (14-XX)
6	Potential theory (31-XX)
5	Several complex variables and analytic spaces (32-XX)
5	Ordinary differential equations (34-XX)
5	Integral equations (45-XX)
5	Statistical mechanics, structure of matter (82-XX)
4	Commutative algebra (13-XX)
4	Difference and functional equations (39-XX)
4	Differential geometry (53-XX)
4	General topology (54-XX)
4	Manifolds and cell complexes (57-XX)
4	Optics, electromagnetic theory (78-XX)
2	Associative rings and algebras (16-XX)
2	Mechanics of particles and systems (70-XX)
2	Geophysics (86-XX)
2	Mathematics education (97-XX)
1	History and biography (01-XX)
1	\(K\)-theory (19-XX)
1	Sequences, series, summability (40-XX)
1	Algebraic topology (55-XX)
1	Astronomy and astrophysics (85-XX)

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