On discrete analytic functions: Products, rational functions and reproducing kernels

被引：22

作者：

Alpay, Daniel ^{[1
]}

Jorgensen, Palle ^{[2
]}

Seager, Ron ^{[3
]}

Volok, Dan ^{[3
]}

机构：

[1] Ben Gurion Univ Negev, Dept Math, POB 653, IL-84105 Beer Sheva, Israel

[2] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

[3] Kansas State Univ, Dept Math, Manhattan, KS 66506 USA

来源：

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING | 2013年 / 41卷 / 1-2期

关键词：

Discrete analytic functions; 2D lattice Z(2); Reproducing kernel Hilbert space; Multipliers; Cauchy integral representation; Difference operators; Lie algebra of operators; Fourier transform; Realizable linear systems; Expandable functions; Rational functions; Cauchy-Riemann equations; Cauchy-Kovalevskaya theorem; Schur analysis; Fock space;

D O I：

10.1007/s12190-012-0608-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a family of discrete analytic functions, called expandable discrete analytic functions, which includes discrete analytic polynomials, and define two products in this family. The first one is defined in a way similar to the CauchyKovalevskaya product of hyperholomorphic functions, and allows us to define rational discrete analytic functions. To define the second product we need a new space of entire functions which is contractively included in the Fock space. We study in this space some counterparts of Schur analysis.

引用

页码：393 / 426

页数：34

共 27 条

[1] Rational hyperholomorphic functions in R4
Alpay, D
Shapiro, M
Volok, D
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2005, 221 (01) : 122 - 149
[2] de Branges Rovnyak spaces and Schur functions: the hyperholomorphic case.
Alpay, D
Shapiro, M
Volok, D
[J]. COMPTES RENDUS MATHEMATIQUE, 2004, 338 (06) : 437 - 442
[3] Alpay D., 2001, SCHUR ALGORITHM REPR
[4] Alpay D., 1997, OPERATOR THEORY ADV, V96
[5] Reproducing kernel spaces of series of Fueter polynomials
Alpay, Daniel
Shapiro, Michael
Volok, Dan
[J]. Operator Theory in Krein Spaces and Nonlinear Eigenvalue Problems, 2006, 162 : 19 - 45
[6] THEORY OF REPRODUCING KERNELS
ARONSZAJN, N
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1950, 68 (MAY) : 337 - 404
[7] Bart H., 1979, OPERATOR THEORY ADV, V1
[8] BRACKX F, 1982, PITMAN RES NOTES, V76
[9] UNBOUNDED DERIVATIONS TANGENTIAL TO COMPACT-GROUPS OF AUTOMORPHISMS
BRATTELI, O
JORGENSEN, PET
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1982, 48 (01) : 107 - 133
[10] Colombo S., 1959, MONOGRAPHIES CTR E B

← 1 2 3 →