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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 9 scientific papers (total in 9 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 (9)
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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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\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 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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