On Higher Regularized Traces of a Differential Operator with Bounded Operator Coeffcient Given in a Finite Interval

TL;DR

This paper derives a higher regularized trace formula for a Sturm-Liouville differential operator with an operator coefficient on a finite interval, advancing spectral analysis techniques.

Contribution

It introduces a novel higher regularized trace formula for Sturm-Liouville operators with operator coefficients, expanding the theoretical framework.

Findings

Established a new trace formula for the operator

Extended spectral analysis methods to operator coefficients

Provided mathematical tools for further spectral studies

Abstract

In this work, a higher regularized trace formula has been found for a regular Sturm-Liouville differential operator with operator coefficient.