(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 $\sum\limits_k[\lambda _k^m-A_m(k)]$, $m \in \mathbb{N}$, 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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