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Funktsional. Anal. i Prilozhen., 2010, Volume 44, Issue 1, Pages 90–96 (Mi faa2975)  

This article is cited in 1 scientific paper (total in 1 paper)

Brief communications

Schwartz Kernel Asymptotics and Regularized Traces of Diffusion Semigroups

S. A. Stepinab

a M. V. Lomonosov Moscow State University
b University of Białystok

Abstract: The relationship between the parametrix of a diffusion type parabolic equation and the path integral representation of its fundamental solution provides an approach to computing the coefficients in the asymptotic expansion of the diffusion kernel constructively. The upper and lower bounds obtained in this paper for the regularized trace of the corresponding evolution semigroup strengthen and supplement the estimates which can be established by other methods.

Keywords: diffusion semigroup, short-time asymptotics, regularized trace, parametrix, Feynman–Kac formula

DOI: https://doi.org/10.4213/faa2975

Full text: PDF file (195 kB)
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English version:
Functional Analysis and Its Applications, 2010, 44:1, 76–80

Bibliographic databases:

UDC: 517.9
Received: 06.02.2008
Revised: 05.02.2008

Citation: S. A. Stepin, “Schwartz Kernel Asymptotics and Regularized Traces of Diffusion Semigroups”, Funktsional. Anal. i Prilozhen., 44:1 (2010), 90–96; Funct. Anal. Appl., 44:1 (2010), 76–80

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. A. Stepin, “Asymptotic estimates for the kernel of the semigroup generated by a perturbation of the biharmonic operator by a potential”, Sb. Math., 203:6 (2012), 893–921  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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