TY - JOUR

T1 - On discrete analytic functions

T2 - Products, rational functions and reproducing kernels

AU - Alpay, Daniel

AU - Jorgensen, Palle

AU - Seager, Ron

AU - Volok, Dan

N1 - Funding Information:
D. Alpay thanks the Earl Katz family for endowing the chair which supported his research. The research of the authors was supported in part by the Binational Science Foundation grant 2010117.

PY - 2013/3/1

Y1 - 2013/3/1

N2 - 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.

AB - 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.

KW - 2D lattice ℤ

KW - Cauchy integral representation

KW - Cauchy-Kovalevskaya theorem

KW - Cauchy-Riemann equations

KW - Difference operators

KW - Discrete analytic functions

KW - Expandable functions

KW - Fock space

KW - Fourier transform

KW - Lie algebra of operators

KW - Multipliers

KW - Rational functions

KW - Realizable linear systems

KW - Reproducing kernel Hilbert space

KW - Schur analysis

UR - http://www.scopus.com/inward/record.url?scp=84873339370&partnerID=8YFLogxK

U2 - 10.1007/s12190-012-0608-2

DO - 10.1007/s12190-012-0608-2

M3 - Article

AN - SCOPUS:84873339370

VL - 41

SP - 393

EP - 426

JO - Journal of Applied Mathematics and Computing

JF - Journal of Applied Mathematics and Computing

SN - 1598-5865

IS - 1-2

ER -