A general trace formula for the differential operator on a segment with the last coefficient perturbed by a finite signed measure

TL;DR

This paper derives a first order trace formula for a regular differential operator on a segment when its last coefficient is perturbed by a finite signed measure, extending the understanding of spectral properties under such perturbations.

Contribution

It introduces a general trace formula applicable to differential operators with measure perturbations, broadening previous results to include finite signed measures.

Findings

Established a first order trace formula for measure-perturbed differential operators

Extended spectral analysis techniques to include finite signed measure perturbations

Provided a framework for analyzing spectral shifts due to measure perturbations

Abstract

A first order trace formula is obtained for a regular differential operator perturbed by a finite signed measure multiplication operator.