FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1998, VOLUME 4, NUMBER 2, PAGES 567-583

Regularized traces of boundary problems in case of multiple roots of characteristic polynomial

A. S. Pechentsov

Abstract

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The boundary problem on a segment for differential equation of $n$ order with coefficients polynomially depending on spectral parameter $\lambda$ is considered. In the general case of multiple roots of Tamarkin's characteristic polynomial the regularized traces, i.e. the sums $\sum$_k[ λ _k^m-A_m(k)], $m\; \in$N, are calculated, where $\lambda$_k are eigenvalues of the problem, and $A$_m(k) are totally defined numbers, ensuring the convergence of series.

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Last modified: June 17, 1998