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Tr. Mat. Inst. 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

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.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2010, 271, 228–245

Bibliographic databases:

Document Type: Article
UDC: 517.9
Received in December 2009

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, Tr. 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 Tr. Mat. Inst. Steklova
\yr 2010
\vol 271
\pages 241--258
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\yr 2010
\vol 271
\pages 228--245
\crossref{https://doi.org/10.1134/S0081543810040176}
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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. 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
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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