FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

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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Last modified: June 17, 1998