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The Schwarz lemma in bicomplex analysis. (English) Zbl 1529.30050

MSC:

30G35 Functions of hypercomplex variables and generalized variables
30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
Full Text: DOI

References:

[1] AlexanderB. Physics in space‐time with scale‐dependent metrics. Phys Lett A. 2013;377(25):1606‐1610. · Zbl 1317.83033
[2] BalankinS. Effective degrees of freedom of a random walk on a fractal. Phys Rev E. 2015;92(6):062146‐1-062146-11.
[3] CatoniF, BoccalettiD, CannataR, CatoniV, NichelattiE, ZampettiP. The Mathematics of Minkowski Space‐Time: With an Introduction to Commutative Hypercomplex Numbers. Birkhäuser Basel; 1998.
[4] BalankinAS, BoryreyesR, Luna‐ElizarrarásME, ShaoiroM. Cantor‐type sets in hyperbolic numbers. Fractals. 2016;24(4):1650051‐1-1650051-12. · Zbl 1357.28008
[5] RichterM, LangeS, BäckerA, KetzmerickR. Visualization and comparison of classical structures and quantum states of four‐dimensional maps. Phys Rev E. 2014;89(2):022902‐1-022902-12.
[6] BanerjeeA. On the quantum mechanics of bicomplex Hamiltonian system. Ann Physics. 2017;377:493‐505. · Zbl 1368.30022
[7] AgarwalR, GoswamiMP, AgarwalRP, VenkataratnamKK, BaleanuD. Solution of maxwell’s wave equations in bicomplex space. Romanian J Phys. 2017;62(5):115.
[8] BanerjeeA, DattaSK, HoqueMA. Fourier transform and its inverse for functions of bicomplex variables. arXiv:1404.4236v1. 2014.
[9] BanerjeeA, DattaSK, HoqueMA. Inverse Laplace transform for bi‐complex variables. arXiv:1403.3313v1. 2014.
[10] BanerjeeA, DebR. Bicomplex modules with indefinite inner product. Adv Appl Clifford Algebras. 2019;29(3):55. · Zbl 1418.30043
[11] BanerjeeA. Bicomplex harmonic and isotonic oscillators: the excited states. Adv Appl Clifford Algebras. 2017;27(3):2321‐2332. · Zbl 1380.30034
[12] AgarwalR, SharmaUP, AgarwalRP. Bicomplex Mittag‐Leffler function and properties. J Nonlinear Sci Appl. 2022;15(1):48‐60.
[13] GoyalR. Bicomplex polygamma function. Tokyo J Math. 2007;30:523‐530. · Zbl 1153.33001
[14] GervaisLR, MarchildonL, RochonD. Finite‐dimensional bicomplex Hilbert spaces. Adv Appl Clifford Algebras. 2011;21(3):568‐581. · Zbl 1237.46009
[15] GervaisLR, MarchildonL, RochonD. Infinite‐dimensional bicomplex hilbert spaces. Ann Funct Anal. 2010;1(2):75‐91. · Zbl 1216.46023
[16] RochonD, TremblayS. Bicomplex quantum mechanics: II. The hilbert space. Adv Appl Clifford Algebras. 2006;16(2):135‐157. · Zbl 1142.81010
[17] KumarR, SinghK, SainiH, KumarS. Bicomplex weighted hardy spaces and bicomplex
[( {C}^{\ast } \]\)‐algebras. Adv Appl Clifford Algebras. 2016;26(1):217‐235. · Zbl 1337.30059
[18] DominicR. A bicomplex Riemann zeta function. Tokyo J Math. 2004;27:357‐369. · Zbl 1075.30025
[19] Luna‐ElizarrarásME, ShapiroM, StruppaDC, VajiacA. Bicomplex Holomorphic Functions: The Algebra, Geometry and Analysis of Bicomplex Numbers, Frontiers in Mathematics. Birkhäuser: Frontiers in mathematics; 2015. · Zbl 1345.30002
[20] Luna‐ElizarrarásME, Pérez‐RegaladoCO, ShapiroM. On the Laurent series for bicomplex holomorphic functions. Complex Var Elliptic Equ. 2017;62(9):1266‐1286. · Zbl 1375.30077
[21] Luna‐ElizarrarásME, Perez‐RegaladoCO, ShapiroM. Singularities of bicomplex holomorphic functions. Math Meth Appl Sci. 2021:1‐16.
[22] Bory‐ReyesJ, Pérez‐RegaladoCO, CesarO, ShapiroM. Cauchy type integral in bicomplex setting and its properties. Complex Anal Oper Theory. 2019;13(6):2541‐2573. · Zbl 1445.30022
[23] YanY, TaoQ. Schwarz lemma in Euclidean spaces. Complex Var Elliptic Equ. 2006;51(7):653‐659. · Zbl 1105.30039
[24] WangH, BianX, LiuH. Möbius transformation and a version of Schwarz lemma in octonionic analysis. Math Meth Appl Sci. 2019;44(1):27‐42. · Zbl 1469.30107
[25] ZhangX. The Schwarz lemma in clifford analysis. Proc Amer Math Soc. 2014;142(4):1237‐1248. · Zbl 1295.30119
[26] ZhangX. The Schwarz lemma for functions with values in
[( C\left({V}_n,0\right) \]\). J Math Anal Appl. 2016;443(2):1130‐1141. · Zbl 1348.30033
[27] ChenH, NieX. Schwarz lemma: the case of equality and an extension. J Geom Anal. 2022;32(3):92. · Zbl 1487.32075
[28] AlpayD, Luna‐ElizarrarásME, ShapiroM, StruppaDC. Basics of Functional Analysis With Bicomplex Scalars, and Bicomplex Schur Analysis. Springer briefs in mathematics Springer; 2014. · Zbl 1319.46001
[29] Luna‐ElizarrarásME, Pérez‐RegaladoCO, ShapiroM. On linear functionals and Hahn‐Banach theorems for hyperbolic and bicomplex modules. Adv Appl Clifford Algebras. 2014;24(4):1105‐1129. · Zbl 1308.30059
[30] Luna‐ElizarrarásME, ShapiroM, StruppaDC, VajiacA. Complex Laplacian and derivatives of bicomplex functions. Complex Anal Oper Theory. 2013;7(5):1675‐1711. · Zbl 1278.30052
[31] Luna‐ElizarrarásME. Integration of functions of a hyperbolic variable. Complex Anal Oper Theory. 2022;16(3):35. · Zbl 1492.30098
[32] EmanuelloJA, NolderCA. Projective compactification in
[( {\mathbb{R}}^{1,1} \]\) and its Möbius geometry. Complex Anal Oper Theory. 2015;9(2):329‐354. · Zbl 1309.30042
[33] GolbergA, Luna‐ElizarrarásME. Hyperbolic conformality in multidimensional hyperbolic spaces. Math Meth Appl Sci. 2020:1‐17.
[34] ChinmayG. Bicomplex Möbius transformation. arXiv.1706.07699. 2018.
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