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

Abstract

In this paper, we investigate the spectrum of the self adjoint operator L defined by L := (-1)(r) d(2r)/dx(2r) + A + Q(x), where A is a self adjoint operator, Q(x) is a nuclear operator in a separable Hilbert space, and we derive asymptotic formulas for the sum of eigenvalues of the operator L.