Schur analysis and discrete analytic functions: Rational functions and co-isometric realizations

TL;DR

This paper introduces rational discrete analytic functions and demonstrates that discrete analytic Schur multipliers can be realized through coisometric operators, advancing the understanding of their structure and properties.

Contribution

It establishes the existence of coisometric realizations for discrete analytic Schur multipliers, a novel result in the field.

Findings

Existence of coisometric realizations for discrete analytic Schur multipliers

Introduction of rational discrete analytic functions

Development of a framework for analyzing discrete analytic functions

Abstract

We define and study rational discrete analytic functions and prove the existence of a coisometric realization for discrete analytic Schur multipliers.