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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 271, Pages 241–258 (Mi tm3245)  
This article is cited in 1 scientific paper (total in 1 paper)

Parametrix, heat kernel asymptotics, and regularized trace of the diffusion semigroup

S. A. Stepinab

a Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia
b Institute of Mathematics, University of Białystok, Białystok, Poland
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Abstract: We establish a relationship between a path integral representation of the heat kernel and the construction of a fundamental solution to a diffusion-type equation by the parametrix method; this relationship is used to find the coefficients of a short-time asymptotic expansion of the heat kernel. We extend the approach proposed to the case of diffusion with drift and obtain two-sided estimates for the regularized trace of the corresponding evolution semigroup.
Received in December 2009
English version:
Proceedings of the Steklov Institute of Mathematics, 2010, Volume 271, Pages 228–245
DOI: https://doi.org/10.1134/S0081543810040176
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: S. A. Stepin, “Parametrix, heat kernel asymptotics, and regularized trace of the diffusion semigroup”, Differential equations and topology. II, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 271, MAIK Nauka/Interperiodica, Moscow, 2010, 241–258; Proc. Steklov Inst. Math., 271 (2010), 228–245
Citation in format AMSBIB
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\by S.~A.~Stepin
\paper Parametrix, heat kernel asymptotics, and regularized trace of the diffusion semigroup
\inbook Differential equations and topology.~II
\bookinfo Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin
\serial Trudy Mat. Inst. Steklova
\yr 2010
\vol 271
\pages 241--258
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3245}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2847768}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2010
\vol 271
\pages 228--245
\crossref{https://doi.org/10.1134/S0081543810040176}
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  • https://www.mathnet.ru/eng/tm3245
  • https://www.mathnet.ru/eng/tm/v271/p241
    • This publication is cited in the following 1 articles:
    1. S. A. Stepin, “Kernel estimates and the regularized trace of the semigroup generated by a potential perturbation of the bi-Laplacian”, Russian Math. Surveys, 66:3 (2011), 635–636  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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