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Mat. Sb., 2012, Volume 203, Number 6, Pages 131–160 (Mi msb7872)  

Asymptotic estimates for the kernel of the semigroup generated by a perturbation of the biharmonic operator by a potential

S. A. Stepinab

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Institute of Mathematics, University of Bialystok

Abstract: Asymptotic formulae and estimates for the integral kernel of the semigroup generated by a perturbation of the bi-Laplacian by a potential are established by the parametrix method. These formulae are found using an approach which is conceptually close to the probabilistic approach used to calculate the coefficients of a short-time expansion for the heat kernel and based on the representation of this kernel as a Wiener integral. As an application, an asymptotic formula for the regularized trace of the operator semigroup under consideration is found.
Bibliography: 19 titles.

Keywords: operator semigroup, parametrix expansion, Born approximation, regularized trace, short-time asymptotics.

DOI: https://doi.org/10.4213/sm7872

Full text: PDF file (574 kB)
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English version:
Sbornik: Mathematics, 2012, 203:6, 893–921

Bibliographic databases:

Document Type: Article
UDC: 517.956.8+517.986.7
MSC: Primary 35C20, 35K25; Secondary 35A17, 47F05
Received: 30.03.2011 and 12.09.2011

Citation: S. A. Stepin, “Asymptotic estimates for the kernel of the semigroup generated by a perturbation of the biharmonic operator by a potential”, Mat. Sb., 203:6 (2012), 131–160; Sb. Math., 203:6 (2012), 893–921

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