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.
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