Transfer functions and local spectral uniqueness for Sturm-Liouville operators, canonical systems and strings

TL;DR

This paper demonstrates that transfer functions are effective tools for establishing local spectral uniqueness in inverse spectral problems related to Sturm-Liouville operators, canonical systems, and strings.

Contribution

It introduces the use of transfer functions to formulate local spectral uniqueness conditions in inverse spectral theory.

Findings

Transfer functions can be used to establish local spectral uniqueness.

The approach applies to Sturm-Liouville operators, canonical systems, and strings.

This method advances inverse spectral problem techniques.

Abstract

It is shown that transfer functions, which play a crucial role in M.G. Krein's study of inverse spectral problems, are a proper tool to formulate local spectral uniqueness conditions.