Trace formulas for fourth order operators on unit interval, II

TL;DR

This paper derives trace formulas for self-adjoint fourth order differential operators on the unit interval, extending classical results from second order operators to higher order cases.

Contribution

It introduces new trace formulas for fourth order operators with Dirichlet boundary conditions, expanding the theoretical framework beyond second order cases.

Findings

Derived explicit trace formulas for fourth order operators

Extended Gelfand–Levitan type formulas to higher order operators

Provided mathematical tools for spectral analysis of fourth order operators

Abstract

We consider self-adjoint fourth order operators on the unit interval with the Dirichlet type boundary conditions. For such operators we determine few trace formulas, similar to the case of Gelfand--Levitan formulas for second order operators.