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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 271, Pages 241–258
(Mi tm3245)
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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.
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, Trudy Mat. Inst. Steklova, 271, MAIK Nauka/Interperiodica, Moscow, 2010, 241–258; Proc. Steklov Inst. Math., 271 (2010), 228–245
Linking options:
https://www.mathnet.ru/eng/tm3245 https://www.mathnet.ru/eng/tm/v271/p241
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Abstract page: | 471 | Full-text PDF : | 77 | References: | 122 |
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