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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Original Russian Text © S.A. Stepin, 2010, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Vol. 271, pp. 241–258.
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Stepin, S.A. Parametrix, heat kernel asymptotics, and regularized trace of the diffusion semigroup. Proc. Steklov Inst. Math. 271, 228–245 (2010). https://doi.org/10.1134/S0081543810040176
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DOI: https://doi.org/10.1134/S0081543810040176