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Mat. Sb., 1999, Volume 190, Number 10, Pages 3–16 (Mi msb430)  

This article is cited in 4 scientific papers (total in 4 papers)

Convergence of regularized traces of powers of the Laplace–Beltrami operator with potential on the sphere $S^n$

A. N. Bobrov, V. E. Podolskii

M. V. Lomonosov Moscow State University

Abstract: For the Laplace–Beltrami operator $-\Delta$ on the sphere $S^n$ perturbed by the operator of multiplication by an infinitely smooth complex-valued function $q$, the convergence without brackets of regularized traces
$$ \sum_k(\mu_k^\alpha -\lambda_k^\alpha-\sum_j\chi_j(\alpha )\lambda_k^{k_j(\alpha)}), $$
is studied, where the $\mu_k$ and the $\lambda_k$ are the eigenvalues of the operators $-\Delta+q$ and $-\Delta$, respectively. Sharp estimates of $\alpha$ in the cases of absolute and conditional convergence are obtained. Explicit formulae for the coefficients $\chi_j$ are obtained for odd potentials $q$.

DOI: https://doi.org/10.4213/sm430

Full text: PDF file (278 kB)
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English version:
Sbornik: Mathematics, 1999, 190:10, 1401–1415

Bibliographic databases:

UDC: 517.956.227
MSC: 58G25, 58G03, 35P20
Received: 07.05.1998

Citation: A. N. Bobrov, V. E. Podolskii, “Convergence of regularized traces of powers of the Laplace–Beltrami operator with potential on the sphere $S^n$”, Mat. Sb., 190:10 (1999), 3–16; Sb. Math., 190:10 (1999), 1401–1415

Citation in format AMSBIB
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\by A.~N.~Bobrov, V.~E.~Podolskii
\paper Convergence of regularized traces of powers of the~Laplace--Beltrami operator with potential on the sphere~$S^n$
\jour Mat. Sb.
\yr 1999
\vol 190
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\pages 3--16
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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. V. A. Sadovnichii, V. E. Podolskii, “Traces of operators”, Russian Math. Surveys, 61:5 (2006), 885–953  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Zykova T.V., “The regularized trace of the perturbed Laplace–Beltrami operator on a certain family of manifolds”, Doklady Mathematics, 83:2 (2011), 225–226  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. T. V. Zykova, “Regularized Trace of the Perturbed Laplace–Beltrami Operator on Two-Dimensional Manifolds with Closed Geodesics”, Math. Notes, 93:3 (2013), 397–411  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. A. I. Kozko, “O nekotorykh priznakakh skhodimosti dlya znakopostoyannykh i znakochereduyuschikhsya ryadov”, Chebyshevskii sb., 18:1 (2017), 123–133  mathnet  crossref  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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