Trace Formula for a High-Order Differential Operator on an Interval under a Perturbation of the Lower-Order Term by a Finite Charge

Abstract

In this paper, a regularized trace formula is obtained for a higher-order differential operator on an interval under a perturbation of the lower-order term by a finite charge. Arbitrary regular boundary conditions and an arbitrary order n ⩾ 3 of the operator are considered. A new effect is discovered: for an even order of the operator, an additional term appears depending on the jump of the charge distribution function at the midpoint of the interval.