The Second Regularized Trace of Even Order Differential Operators with Operator Coefficient

TL;DR

This paper studies the spectrum of a self-adjoint differential operator with operator coefficients in a Hilbert space and derives asymptotic formulas for the sum of its eigenvalues.

Contribution

It introduces new asymptotic formulas for the second regularized trace of even order differential operators with operator coefficients.

Findings

Derived asymptotic formulas for eigenvalue sums

Analyzed spectral properties of operator-coefficient differential operators

Extended trace formulas to higher-order operators

Abstract

In this paper, we investigate the spectrum of the self adjoint differential operator with operator coefficitent in a separable Hilbert space. We also derive asymptotic formulas for the sum of eigenvalues of this operator.