On discrete analytic functions: Products, Rational Functions, and some Associated Reproducing Kernel Hilbert Spaces
Functional Analysis
2012-08-21 v1 Complex Variables
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.
Cite
@article{arxiv.1208.3699,
title = {On discrete analytic functions: Products, Rational Functions, and some Associated Reproducing Kernel Hilbert Spaces},
author = {Daniel Alpay and Palle Jorgensen and Ron Seager and Dan Volok},
journal= {arXiv preprint arXiv:1208.3699},
year = {2012}
}