On explicit inversion of a subclass of operators with $D$-difference kernels and Weyl theory of the corresponding canonical systems

TL;DR

This paper derives explicit inversion formulas for a specific class of integral operators with D-difference kernels, especially positive ones, and applies these results to solve inverse problems for canonical systems using Weyl functions.

Contribution

It provides new explicit inversion formulas for D-difference kernel operators and applies them to inverse problems in canonical systems using Weyl theory.

Findings

Explicit inversion formulas for a subclass of D-difference kernel operators.

Detailed treatment of positive operators within this class.

Application to inverse problems for canonical systems using Weyl functions.

Abstract

Explicit inversion formulas for a subclass of integral operators with $D$-difference kernels on a finite interval are obtained. A case of the positive operators is treated in greater detail. An application to the inverse problem to recover canonical system from a Weyl function is given.