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On the solution of the inverse problem for a class of canonical systems corresponding to matrix string equations

Alexander Sakhnovich

Abstract

We consider canonical systems (with $2p\times 2p$ Hamiltonians $H(x)\geq 0$), which correspond to matrix string equations. Direct and inverse problems are solved in terms of Titchmarsh--Weyl and spectral matrix functions and related $S$-nodes. Procedures for solving inverse problems are given.

On the solution of the inverse problem for a class of canonical systems corresponding to matrix string equations

Abstract

We consider canonical systems (with Hamiltonians ), which correspond to matrix string equations. Direct and inverse problems are solved in terms of Titchmarsh--Weyl and spectral matrix functions and related -nodes. Procedures for solving inverse problems are given.

Paper Structure

This paper contains 5 sections, 74 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Weyl functions
  4. Inverse problem
  5. Spectral matrix functions: direct and inverse problems