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

Daniel Alpay; Palle Jorgensen; Ron Seager; Dan Volok

doi:10.1007/s12190-012-0608-2

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

Journal article

Peer reviewed

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

Daniel Alpay, Palle Jorgensen, Ron Seager and Dan Volok

Journal of Applied Mathematics and Computing, Vol.41(1), pp.393-426

03/2013

DOI: 10.1007/s12190-012-0608-2

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https://digitalcommons.chapman.edu/scs_articles/431View

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Abstract

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 Cauchy-Kovalevskaya 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.

Mathematics

Discrete analytic functions

Computational Mathematics and Numerical Analysis

Reproducing kernel Hilbert space

Multipliers

Fock space

Cauchy integral representation

Lie algebra of operators

Fourier transform

Theory of Computation

2 D lattice ℤ 2

Schur analysis

Mathematics of Computing

Expandable functions

30G25, 30H20, 32A26, 43A22, 46E22, 46L08, 47B32, 47B39

Realizable linear systems

Appl.Mathematics/Computational Methods of Engineering

Rational functions

Cauchy-Kovalevskaya theorem

Difference operators

Cauchy-Riemann equations

20G43

Details

Title: Subtitle: On discrete analytic functions: Products, rational functions and reproducing kernels
Creators: Daniel Alpay - Department of Mathematics Ben Gurion University of the Negev P.O.B. 653 Be’er Sheva 84105 Israel
Palle Jorgensen - Department of Mathematics The University of Iowa 14 MLH Iowa City IA 52242-1419 USA
Ron Seager - Mathematics Department Kansas State University 138 Cardwell Hall Manhattan KS 66506 USA
Dan Volok - Mathematics Department Kansas State University 138 Cardwell Hall Manhattan KS 66506 USA
Resource Type: Journal article
Publication Details: Journal of Applied Mathematics and Computing, Vol.41(1), pp.393-426
DOI: 10.1007/s12190-012-0608-2
ISSN: 1598-5865
eISSN: 1865-2085
Publisher: Springer-Verlag; Berlin/Heidelberg
Language: English
Date published: 03/2013
Academic Unit: Mathematics
Record Identifier: 9983985969402771

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