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Kamiński, Andrzej (ed.) et al., Linear and non-linear theory of generalized functions and its applications. Proceedings of the Banach Center conference, Bȩdlewo, Poland, September 2–8, 2007. Warszawa: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-07-2/pbk). Banach Center Publications 88, 229-241 (2010).

MSC: 46F05 46F12 44A10

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Abouelaz, Ahmed

New inversion formulas for discrete Radon transform $\mathbb{Z}^n$. (English) Zbl 1201.44003

Afr. J. Math. Phys. 6, No. 1, 13-31, Article No. 0801 (2008).

MSC: 44A12 46F12

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Abanin, A. V.

$ \Omega$-ultradistributions. (English. Russian original) Zbl 1162.46023

Izv. Math. 72, No. 2, 207-240 (2008); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 72, No. 2, 3-38 (2008).

Reviewer: Rüdiger W. Braun (Düsseldorf)

MSC: 46F05 46A13

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Li, Chenkuan; Zhang, Yang; Aguirre, Manuel; Tang, Ricky

The product of analytic functionals in ${\mathcal Z}'$. (English) Zbl 1159.46022

J. Korean Math. Soc. 45, No. 2, 455-466 (2008).

Reviewer: Adem Kilicman (Serdang Selangor)

MSC: 46F10

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Dryanov, D.

Sobolev type decomposition of Paley-Wiener-Schwartz space with application to sampling theory. (English) Zbl 1224.94012

Serdica Math. J. 33, No. 4, 411-432 (2007).

MSC: 94A12 94A20 30D20 41A05

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Nemzer, Dennis

Paley-Wiener theorems for trigonometric series. (English) Zbl 1268.42007

J. Indian Math. Soc., New Ser. 74, No. 1-2, 115-123 (2007).

MSC: 42A32 30D15 44A40 46F10

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Soloviev, M. A.

Axiomatic formulations of nonlocal and noncommutative field theories. (English) Zbl 1177.81085

Theor. Math. Phys. 147, No. 2, 660-669 (2006); translation from Teor. Mat. Fiz. 147, No. 2, 257-269 (2006).

MSC: 81T05

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Banerji, P. K.; Al-Omari, S. K.; Debnath, Lokenath

Tempered distributional Fourier sine (cosine) transform. (English) Zbl 1131.42003

Integral Transforms Spec. Funct. 17, No. 11, 759-768 (2006).

Reviewer: Boris Rubin (Baton Rouge)

MSC: 42A38 46F05

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Hoskins, R. F.; Sousa Pinto, J.

Theories of generalised functions. Distributions, ultradistributions and other generalised functions. Revised edition of the 1994 original. (English) Zbl 1101.46001

Chichester: Horwood Publishing (ISBN 1-898563-98-5/pbk). xii, 293 p. (2005).

Reviewer: Antoine Delcroix (Pointe-a-Pitre)

MSC: 46-02 46F30 03H05 46F05 46F10

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Andersen, Nils Byrial

A simple proof of a Paley-Wiener type theorem for the Chébli-Triméche transform. (English) Zbl 1075.46036

Publ. Math. Debr. 64, No. 3-4, 473-479 (2004).

MSC: 46F12

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Lyalikova, E. R.

On analogs of Borel and Whitney theorems. (Russian) Zbl 1010.46035

Izv. Vyssh. Uchebn. Zaved., Sev.-Kavk. Reg., Estestv. Nauki 2002, No. 1, 28-30 (2002).

MSC: 46E35 58C25

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Smirnov, A. G.; Solov’ev, M. A.

Spectral properties of Wick power series for a free field with an indefinite metric. (English. Russian original) Zbl 1032.81535

Theor. Math. Phys. 125, No. 1, 1349-1362 (2000); translation from Teor. Mat. Fiz. 125, No. 1, 57-73 (2000).

MSC: 81T10 81T05

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Gussi, G.

Topics in analysis and distribution theory. (English) Zbl 0991.46022

Seminar Series in Mathematics: Analysis. 3. Constantza: Ovidius University. iv, 242 p. (1999).

Reviewer: Susanne Dierolf (Trier)

MSC: 46F10 46-02 30-02 31-02 46G05 46E15

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Cho, Jonggyu; Kim, Kwang Whoi

Real version of Paley-Wiener-Schwartz theorem for ultradistributions with ultradifferentiable singular support. (English) Zbl 0935.46038

Bull. Korean Math. Soc. 36, No. 3, 483-493 (1999).

MSC: 46F15 46F12 42B10 46F05

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Ha Huy Bang

The Paley-Wiener-Schwartz theorem for nonconvex domains. (English) Zbl 0922.46039

Sunada, Toshikazu (ed.) et al., Functional analysis and global analysis. Proceedings of the conference, Manila, Philippines, October 20–26, 1996. Singapore: Springer. 14-30 (1998).

MSC: 46F12

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Ramanathan, Jayakumar

Methods of applied Fourier analysis. (English) Zbl 0926.94004

Applied and Numerical Harmonic Analysis. Boston, MA: Birkhäuser. xii, 329 p. (1998).

Reviewer: W.Schempp (Siegen)

MSC: 94A12 42-01 94-01 65-01 93-01 42C40 65T60 65T50 60G25 60G35

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Sharin, S. V.

The Paley-Wiener theorem for Schwartz distributions with supports on a half-line. (English. Ukrainian original) Zbl 0926.46033

J. Math. Sci., New York 96, No. 2, 2985-2987 (1999); translation from Mat. Metody Fiz.-Mekh. Polya 40, No. 4, 54-57 (1997).

Reviewer: V.G.Miladzhanov (Andizhan)

MSC: 46F12 46F20

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Ha Huy Bang

Paley-Wiener-Schwartz type theorems. (English. Russian original) Zbl 0906.46031

Proc. Steklov Inst. Math. 214, 291-311 (1996); translation from Tr. Mat. Inst. Steklova 214, 298-319 (1997).

MSC: 46F12

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Ehrenpreis, Leon

The role of Paley-Wiener theory in partial differential equations. (English) Zbl 0909.35032

Jerison, David (ed.) et al., The legacy of Norbert Wiener: a centennial symposium. In honor of the 100th anniversary of Norbert Wiener’s birth, October 8-14, 1994, Cambridge, MA, USA. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 60, 71-83 (1997).

Reviewer: R.Johnson (College Park)

MSC: 35E20 43A85 42B10 32A15

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Soloviev, M. A.

Wick-ordered entire functions of the indefinite metric free field. (English) Zbl 0897.46020

Lett. Math. Phys. 41, No. 3, 265-277 (1997).

Reviewer: D.Zarnadze (Tbilisi)

MSC: 46F05 81-05 46F15 81S99

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Matsumoto, Kengo

**Distributions on $C^*$-algebras associated with $\mathbb{R}^ n$-actions.** (English) Zbl 0873.46034

Proc. Lond. Math. Soc., III. Ser. 74, No. 2, 444-480 (1997).

Reviewer: K.Matsumoto (Kiryu)

MSC: 46L55 46F25 46L89

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Bang, Ha Huy

Functions with bounded spectrum. (English) Zbl 0828.42009

Trans. Am. Math. Soc. 347, No. 3, 1067-1080 (1995).

MSC: 42B10 26D10 46E30

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Szmydt, Zofia; Ziemian, Bogdan

Between the Paley-Wiener theorem and the Bochner tube theorem. (English) Zbl 0830.46034

Ann. Pol. Math. 60, No. 3, 299-304 (1995).

MSC: 46F12

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Soloviev, M. A.

On a spectral condition for infrared singular quantum fields. (English. Russian original) Zbl 0888.46052

Theor. Math. Phys. 105, No. 3, 1520-1524 (1995); translation from Teor. Mat. Fiz. 105, No. 3, 405-411 (1995).

MSC: 46N50 81T05

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Bouaziz, Abderrazak

Orbital integrals on reductive Lie groups. (Intégrales orbitales sur les groupes de Lie réductifs.) (French) Zbl 0832.22017

Ann. Sci. Éc. Norm. Supér. (4) 27, No. 5, 573-609 (1994).

Reviewer: W.M.McGovern (Seattle)

MSC: 22E30 43A80

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Hoskins, R. F.; Sousa Pinto, J.

Distributions, ultradistributions and other generalised functions. (English) Zbl 0831.46038

Ellis Horwood Series in Mathematics and its Applications. New York, NY: Ellis Horwood. xiv, 300 p. (1994).

Reviewer: L.S.Dube (Quebec)

MSC: 46F12 46-01 46F05 46F10

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Cui, Shangbin; Ma, Yulan

Global regularity of solutions for non-hypoelliptic linear partial differential equations and systems with constant coefficients. (Chinese. English summary) Zbl 0875.35017

J. Lanzhou Univ., Nat. Sci. 29, No. 3, 1-6 (1993).

MSC: 35E20 35D10

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Anker, Jean-Philippe

The spherical Fourier transform of rapidly decreasing functions. A simple proof of a characterization due to Harish-Chandra, Helgason, Trombi, and Varadarajan. (English) Zbl 0732.43006

J. Funct. Anal. 96, No. 2, 331-349 (1991).

Reviewer: F. Rouvière (Nice)

MSC: 43A90 43A15 22E46

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Mandache, Niculae

A Paley-Wiener theorem and pseudolocal operators. (English) Zbl 0752.46024

Rev. Roum. Math. Pures Appl. 35, No. 4, 321-328 (1990).

MSC: 46F12 47G30 46M05

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Braun, R. W.; Meise, R.; Taylor, B. A.

Ultradifferentiable functions and Fourier analysis. (English) Zbl 0735.46022

Result. Math. 17, No. 3-4, 206-237 (1990).

Reviewer: S.Dierolf (Trier)

MSC: 46F05 46E10 46F10 42B10

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Ha Huy Bang

A property of infinitely differentiable functions. (English) Zbl 0707.26015

Proc. Am. Math. Soc. 108, No. 1, 73-76 (1990).

Reviewer: W.Pleśniak

MSC: 26E10

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Betori, W.; Faraut, J.; Pagliacci, M.

An inversion formula for the Radon transform on trees. (English) Zbl 0651.43003

Math. Z. 201, No. 3, 327-337 (1989).

Reviewer: G.van Dijk

MSC: 43A32 05C05

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Full Text: DOI EuDML

Kamthan, P. K.; Gupta, M.

Schauder bases: behaviour and stability. (English) Zbl 0682.46001

Pitman Monographs and Surveys in Pure and Applied Mathematics, 42. Harlow (UK): Longman Scientific & Technical; New York: Wiley. 514 p. £42.50 (1988).

Reviewer: T.Precupanu

MSC: 46A35 46-02 46A45 46A13 46A11 47B10

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Gangolli, Ramesh; Varadarajan, Veeravalli S.

Harmonic analysis of spherical functions on real reductive groups. (English) Zbl 0675.43004

Ergebnisse der Mathematik und ihrer Grenzgebiete, 101. Berlin etc.: Springer-Verlag. xiv, 365 p. (1988).

Reviewer: M.Flensted-Jensen

MSC: 43A90 22E30 43-02 43A30 33C80 22-02

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Llavona, José G.

Approximation of continuously differentiable functions. (English) Zbl 0642.41001

North-Holland Mathematics Studies, 130. Notas de Matemática (112). Amsterdam etc.: North-Holland. XIV, 241 p.; $ 48.00; Dfl. 120.00 (1986).

Reviewer: F.Verhulst

MSC: 41-02 41A65 42A38

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Delorme, Patrick

Formules limites et formules asymptotiques pour les multiplicités dans $L^ 2(G/\Gamma)$. (Limit formulas and asymptotic formulas for the multiplicities in $L^ 2(G/\Gamma))$. (French) Zbl 0623.22012

Duke Math. J. 53, 691-731 (1986).

Reviewer: R.Miatello

MSC: 22E45 22E46 22E40

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Kim, Jung Soo; Kim, Dohan; Kim, June Gi

An analogue of Paley-Wiener-Schwartz theorem for analytic singular support. (English) Zbl 0602.42012

Bull. Korean Math. Soc. 23, 47-50 (1986).

Reviewer: K.Srivastava

MSC: 42A38

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Misra, O. P.; Lavoine, J. L.

Transform analysis of generalized functions. (English) Zbl 0583.46032

North-Holland Mathematics Studies, 119. Notas de Matemática (106). Amsterdam-New York-Oxford: North-Holland. XIV, 332 p. $ 48.25; Dfl. 140.00 (1986).

Reviewer: R.D.Carmichael

MSC: 46F12 46-02 46F10 46F05

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Colombeau, J. F.; Paques, O. T. W.

Structure of spaces of $C^{\infty}-functions$ on nuclear spaces. (English) Zbl 0543.46027

Isr. J. Math. 45, 17-32 (1983).

Reviewer: P.Raboin

MSC: 46G20 46A08 46A13 46A11 46M40

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Tadic, M.

Harmonic analysis of spherical functions on reductive groups over p-adic fields. (English) Zbl 0513.43005

Pac. J. Math. 109, 215-235 (1983).

MSC: 43A30 22E50

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Colombeau, J. F.; Paques, O. W.

Finite-difference partial differential equations in normed and locally convex spaces. (English) Zbl 0533.46027

Functional analysis, holomorphy and approximation theory, Proc. Semin., Rio de Janeiro 1980, North-Holland Math. Stud. 71, 201-214 (1982).

Reviewer: L.Nachbin

MSC: 46F25 46G20 46E10

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Friedlander, F. G.

Introduction to the theory of distributions. (English) Zbl 0499.46020

Cambridge etc.: Cambridge University Press. III, 157 p. $ 17.50; £6.95 (1982).

MSC: 46F10 46F05 46F12 46-01 35D05

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Ansemil, J. M.; Colombeau, J. F.

The Paley-Wiener-Schwartz isomorphism in nuclear spaces. (English) Zbl 0485.46020

Rev. Roum. Math. Pures Appl. 26, 169-181 (1981).

MSC: 46F25 46A08 46A13 46A11

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Vladimirov, Vasilij Sergeevich

Le distribuzioni nella fisica matematica. Traduzione del russo di Renato Betti. (Italian) Zbl 0456.46033

Mosca: Edizioni Mir. 320 p. (1981).

MSC: 46F12 46-01 46F05 35D05 65H10 46F10

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Maurin, Krzysztof

Analysis. Part II: Integration, distributions, holomorphic functions, tensor and harmonic analysis. Rev. transl. of ”Analiza”. (English) Zbl 0432.46001

Dordrecht, Boston, London: D. Reidel Publishing Company. Warsaw: PWN - Polish Scientific Publishers. XVII, 829 p. (1980).

MSC: 46-02 28-02 30-02 32-02 28C05 28C10 28C20 30F10 30F15 30F35 32A10 32A20 30D30 32A17 32A27 46A13 46A11 46F05 46F10 46F12 46J20 54D20 54D15

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Schempp, Walter

Schwartz kernels on Siegel II domain. (English) Zbl 0417.46027

Math. Z. 171, 101-112 (1980).

MSC: 46E20 46F12 46J15 42B10 42B30

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Full Text: DOI EuDML

Vladimirov, V. S.

Generalized functions in mathematical physics. Transl. from the 2nd Russian edition by G. Yankovskij. (English) Zbl 0515.46034

Moscow: Mir Publishers. 362 p. R. 2.35 (1979).

MSC: 46F10 46-02 46F05 46F12 35D05 35D10 46N99

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Vladimirov, V. S.

Generalized functions in mathematical physics. (Obobshchennye funktsii v matematicheskoj fizike). 2nd ed., correct. and suppl. (Russian) Zbl 0515.46033

Sovremennye Fiziko-Tekhnicheskie Problemy. Moskva: “Nauka”. 319 p. R. 1.60 (1979).

MSC: 46F10 46-02 46F05 46F12 35D05 35D10 46N99

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Ehrenpreis, Leon

Edge of the wedge theorem for partial differential equations. (English) Zbl 0427.35005

Harmonic analysis in Euclidean spaces, Part 2, Williamstown/ Massachusetts 1978, Proc. Symp. Pure Math., Vol. 35, 203-212 (1979).

MSC: 35A99 35A22 42A38 46F10

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Kawazoe, Takeshi

An analogue of Paley-Wiener theorem on rank 1 semisimple Lie groups. II. (English) Zbl 0426.43013

Tokyo J. Math. 2, 409-421 (1979).

MSC: 43A80 22E30 22E46

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Full Text: DOI

Abuabara, Teofilo

The theorem of Paley-Wiener-Schwartz in infinite dimension. (Portuguese) Zbl 0412.46039

An. Acad. Bras. Cienc. 51, 35-49 (1979).

MSC: 46F25 46F12 46F10 46G20 46E10 46G10

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Abuabara, Teofilo

A version of the Paley-Wiener-Schwartz theorem in infinite dimensions. (English) Zbl 0404.46024

Advances in Holomorphy, Proc. Semin., Rio de Janeiro 1977, North-Holland Math. Stud. 34, 1-29 (1979).

MSC: 46F25 46E10 46G20

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Vladimirov, V.

Distributions en physique mathématique. Traduit du russe par Irina Petrova. (French) Zbl 0403.46036

Moscou: Editions Mir. 280 p. R. 2.04 (1979).

MSC: 46F12 46-01 46F05 35D05 65H10 46F10

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Abuabara, Teofilo

On the Paley-Wiener-Schwartz theorem in infinite dimensions. (English) Zbl 0402.46030

Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 63, 192-194 (1978).

MSC: 46F25 46G20

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Found 58 Documents (Results 1–58)

Paley-Wiener-Schwartz type theorem for ultradistributions on an unbounded closed convex set. (English. Russian original) Zbl 1484.46047

Analogs of the spherical transform in the hyperbolic plane. (English. Russian original) Zbl 1490.46041

A criterion for the compactness of the support of a generalized function (distribution) in terms of the Fourier-Laplace transform. (English. Russian original) Zbl 1314.30002

Range of \(\mathcal D(\mathbb R)\) by integral transforms associated to the Bessel-Struve operator. (English) Zbl 1314.42006

Laplace ultradistributions supported by a cone. (English) Zbl 1202.46046

New inversion formulas for discrete Radon transform \(\mathbb{Z}^n\). (English) Zbl 1201.44003

\( \Omega\)-ultradistributions. (English. Russian original) Zbl 1162.46023

The product of analytic functionals in \({\mathcal Z}'\). (English) Zbl 1159.46022

Sobolev type decomposition of Paley-Wiener-Schwartz space with application to sampling theory. (English) Zbl 1224.94012

Paley-Wiener theorems for trigonometric series. (English) Zbl 1268.42007

Axiomatic formulations of nonlocal and noncommutative field theories. (English) Zbl 1177.81085

Tempered distributional Fourier sine (cosine) transform. (English) Zbl 1131.42003

Theories of generalised functions. Distributions, ultradistributions and other generalised functions. Revised edition of the 1994 original. (English) Zbl 1101.46001

A simple proof of a Paley-Wiener type theorem for the Chébli-Triméche transform. (English) Zbl 1075.46036

On analogs of Borel and Whitney theorems. (Russian) Zbl 1010.46035

Spectral properties of Wick power series for a free field with an indefinite metric. (English. Russian original) Zbl 1032.81535

Topics in analysis and distribution theory. (English) Zbl 0991.46022

Real version of Paley-Wiener-Schwartz theorem for ultradistributions with ultradifferentiable singular support. (English) Zbl 0935.46038

The Paley-Wiener-Schwartz theorem for nonconvex domains. (English) Zbl 0922.46039

Methods of applied Fourier analysis. (English) Zbl 0926.94004

The Paley-Wiener theorem for Schwartz distributions with supports on a half-line. (English. Ukrainian original) Zbl 0926.46033

Paley-Wiener-Schwartz type theorems. (English. Russian original) Zbl 0906.46031

The role of Paley-Wiener theory in partial differential equations. (English) Zbl 0909.35032

Wick-ordered entire functions of the indefinite metric free field. (English) Zbl 0897.46020

Distributions on \(C^*\)-algebras associated with \(\mathbb{R}^ n\)-actions. (English) Zbl 0873.46034

Functions with bounded spectrum. (English) Zbl 0828.42009

Between the Paley-Wiener theorem and the Bochner tube theorem. (English) Zbl 0830.46034

On a spectral condition for infrared singular quantum fields. (English. Russian original) Zbl 0888.46052

Orbital integrals on reductive Lie groups. (Intégrales orbitales sur les groupes de Lie réductifs.) (French) Zbl 0832.22017

Distributions, ultradistributions and other generalised functions. (English) Zbl 0831.46038

Global regularity of solutions for non-hypoelliptic linear partial differential equations and systems with constant coefficients. (Chinese. English summary) Zbl 0875.35017

The spherical Fourier transform of rapidly decreasing functions. A simple proof of a characterization due to Harish-Chandra, Helgason, Trombi, and Varadarajan. (English) Zbl 0732.43006

A Paley-Wiener theorem and pseudolocal operators. (English) Zbl 0752.46024

Ultradifferentiable functions and Fourier analysis. (English) Zbl 0735.46022

A property of infinitely differentiable functions. (English) Zbl 0707.26015

An inversion formula for the Radon transform on trees. (English) Zbl 0651.43003

Schauder bases: behaviour and stability. (English) Zbl 0682.46001

Harmonic analysis of spherical functions on real reductive groups. (English) Zbl 0675.43004

Approximation of continuously differentiable functions. (English) Zbl 0642.41001

Formules limites et formules asymptotiques pour les multiplicités dans \(L^ 2(G/\Gamma)\). (Limit formulas and asymptotic formulas for the multiplicities in \(L^ 2(G/\Gamma))\). (French) Zbl 0623.22012

An analogue of Paley-Wiener-Schwartz theorem for analytic singular support. (English) Zbl 0602.42012

Transform analysis of generalized functions. (English) Zbl 0583.46032

Structure of spaces of \(C^{\infty}-functions\) on nuclear spaces. (English) Zbl 0543.46027

Harmonic analysis of spherical functions on reductive groups over p-adic fields. (English) Zbl 0513.43005

Finite-difference partial differential equations in normed and locally convex spaces. (English) Zbl 0533.46027

Introduction to the theory of distributions. (English) Zbl 0499.46020

The Paley-Wiener-Schwartz isomorphism in nuclear spaces. (English) Zbl 0485.46020

Le distribuzioni nella fisica matematica. Traduzione del russo di Renato Betti. (Italian) Zbl 0456.46033

Analysis. Part II: Integration, distributions, holomorphic functions, tensor and harmonic analysis. Rev. transl. of ”Analiza”. (English) Zbl 0432.46001

Schwartz kernels on Siegel II domain. (English) Zbl 0417.46027

Generalized functions in mathematical physics. Transl. from the 2nd Russian edition by G. Yankovskij. (English) Zbl 0515.46034

Generalized functions in mathematical physics. (Obobshchennye funktsii v matematicheskoj fizike). 2nd ed., correct. and suppl. (Russian) Zbl 0515.46033

Edge of the wedge theorem for partial differential equations. (English) Zbl 0427.35005

An analogue of Paley-Wiener theorem on rank 1 semisimple Lie groups. II. (English) Zbl 0426.43013

The theorem of Paley-Wiener-Schwartz in infinite dimension. (Portuguese) Zbl 0412.46039

A version of the Paley-Wiener-Schwartz theorem in infinite dimensions. (English) Zbl 0404.46024

Distributions en physique mathématique. Traduit du russe par Irina Petrova. (French) Zbl 0403.46036

On the Paley-Wiener-Schwartz theorem in infinite dimensions. (English) Zbl 0402.46030

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**Distributions on \(C^*\)-algebras associated with \(\mathbb{R}^ n\)-actions.** (English) Zbl 0873.46034