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Fundam. Prikl. Mat., 1998, Volume 4, Issue 2, Pages 567–583 (Mi fpm319)  

This article is cited in 3 scientific papers (total in 3 papers)

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

A. S. Pechentsov

M. V. Lomonosov Moscow State University

Abstract: 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.

Full text: PDF file (606 kB)

Bibliographic databases:
UDC: 517.94
Received: 01.03.1998

Citation: A. S. Pechentsov, “Regularized traces of boundary problems in case of multiple roots of characteristic polynomial”, Fundam. Prikl. Mat., 4:2 (1998), 567–583

Citation in format AMSBIB
\Bibitem{Pec98}
\by A.~S.~Pechentsov
\paper Regularized traces of boundary problems in case of multiple roots of characteristic polynomial
\jour Fundam. Prikl. Mat.
\yr 1998
\vol 4
\issue 2
\pages 567--583
\mathnet{http://mi.mathnet.ru/fpm319}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1801175}
\zmath{https://zbmath.org/?q=an:0963.34009}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Pechentsov, AS, “Regularized traces of differential operators. The Lidskii-Sadovnichii method”, Differential Equations, 35:4 (1999), 490  mathnet  mathscinet  zmath  isi
    2. Pechentsov A.S., “Regularized traces of differential operators”, Recent Advances in Operator Theory, Opeator Algebras, and their Applications, Operator Theory : Advances and Applications, 153, 2005, 211–227  crossref  mathscinet  zmath  isi
    3. A. I. Kozko, “O nekotorykh priznakakh skhodimosti dlya znakopostoyannykh i znakochereduyuschikhsya ryadov”, Chebyshevskii sb., 18:1 (2017), 123–133  mathnet  crossref  elib
  • Фундаментальная и прикладная математика
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