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Matematicheskie Zametki, 2005, Volume 77, Issue 3, Pages 434–448
DOI: https://doi.org/10.4213/mzm2504 (Mi mzm2504) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Asymptotics of the eigenvalues and the formula for the trace of perturbations of the Laplace operator on the sphere $\mathbb S^2$

V. A. Sadovnichiia, Z. Yu. Fazullinb

a M. V. Lomonosov Moscow State University
b Bashkir State University
Full-text PDF (226 kB) Citations (10)
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DOI: https://doi.org/10.4213/mzm2504
Abstract: In this paper, we study the asymptotics of the eigenvalues of the Laplace operator perturbed by an arbitrary bounded operator on the sphere $\mathbb S^2$. For the first time, for the partial differential operator of second order, the leading term of the second correction of perturbation theory is obtained. A connection between the coefficient of the second term of the asymptotics of the eigenvalues and the formula for the traces of the operator under consideration is established.
Received: 18.11.2003
Revised: 08.07.2004
English version:
Mathematical Notes, 2005, Volume 77, Issue 3, Pages 400–413
DOI: https://doi.org/10.1007/s11006-005-0039-6
Bibliographic databases:
UDC: 517.946
Language: Russian
Citation: V. A. Sadovnichii, Z. Yu. Fazullin, “Asymptotics of the eigenvalues and the formula for the trace of perturbations of the Laplace operator on the sphere $\mathbb S^2$”, Mat. Zametki, 77:3 (2005), 434–448; Math. Notes, 77:3 (2005), 400–413
Citation in format AMSBIB
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\by V.~A.~Sadovnichii, Z.~Yu.~Fazullin
\paper Asymptotics of the eigenvalues and the formula for the trace of perturbations of the Laplace operator on the sphere~$\mathbb S^2$
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\vol 77
\issue 3
\pages 434--448
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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