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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:
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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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V. A. Sadovnichii, V. E. Podolskii, “Traces of operators”, Russian Math. Surveys, 61:5 (2006), 885–953
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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
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A. I. Kozko, “O nekotorykh priznakakh skhodimosti dlya znakopostoyannykh i znakochereduyuschikhsya ryadov”, Chebyshevskii sb., 18:1 (2017), 123–133
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