Titchmarsh-Weyl theory for vector valued Schrodinger operators

TL;DR

This paper extends Titchmarsh-Weyl theory to vector-valued discrete Schrödinger operators, analyzing their Weyl functions and geometric properties in complex analysis.

Contribution

It introduces a novel extension of Titchmarsh-Weyl theory to vector-valued operators and characterizes the associated Weyl functions in the Siegel upper half space.

Findings

Weyl m-functions map the upper half plane to the Siegel upper half space

Discussion of Weyl disk and circle for these operators

Establishment of the theoretical framework for vector-valued Schrödinger operators

Abstract

We develop the Titchmarsh-Weyl theory for vector-valued discrete Schr\"odinger operators and show that the Weyl $m$ functions associated with these operators map complex upper half plane to the Siegel upper half space. We also discuss about the Weyl disk and Weyl circle corresponding to these operators.