Generalised canonical systems related to matrix string equations: corresponding structured operators and high-energy asymptotics of the Weyl functions

TL;DR

This paper derives high-energy asymptotics for Weyl functions of generalized canonical systems, extending prior results, and explores related structured operators and new identities in the matrix-valued amplitude function.

Contribution

It introduces high-energy asymptotics for Weyl functions of generalized canonical systems and investigates associated structured operators and novel identities.

Findings

High-energy asymptotics of Weyl functions derived

New identity for matrix-valued amplitude function established

Structured operators analyzed in the context of generalized systems

Abstract

We obtain high energy asymptotics of Titchmarsh-Weyl functions of the generalised canonical systems generalising in this way a seminal Gesztesy-Simon result. The matrix valued analog of the amplitude function satisfies in this case an interesting new identity. The corresponding structured operators are studied as well.