Discrete analytic Schur functions

TL;DR

This paper introduces a new class of discrete analytic functions called Schur functions on the integer lattice, providing explicit formulas for Blaschke factors and solving a fundamental interpolation problem.

Contribution

It defines the discrete analytic Schur class and derives explicit forms for Blaschke factors, addressing a key interpolation problem in discrete complex analysis.

Findings

Explicit form of discrete analytic Blaschke factors

Solution to the basic interpolation problem for these functions

Introduction of the Schur class in the discrete setting

Abstract

We introduce the Schur class of functions, discrete analytic on the integer lattice in the complex plane. As a special case, we derive the explicit form of discrete analytic Blaschke factors and solve the related basic interpolation problem.