Geodesic
Asymptotic estimates for the kernel of the semigroup generated by a~perturbation of the biharmonic operator by a~potential
Sbornik. Mathematics, Tome 203 (2012) no. 6, pp. 893-921

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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. 
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     title = {Asymptotic estimates for the kernel of the semigroup generated by a~perturbation of the biharmonic operator by a~potential},
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S. A. Stepin. Asymptotic estimates for the kernel of the semigroup generated by a~perturbation of the biharmonic operator by a~potential. Sbornik. Mathematics, Tome 203 (2012) no. 6, pp. 893-921. http://geodesic.mathdoc.fr/item/SM_2012_203_6_a5/