Abstract
In view of the asymptotic analysis to be carried out (for evolutionary semigroups beyond the diffusion type class) we first outline the path integral approach to the study of heat kernel asymptotics and heat trace estimations. Within this approach for the case of diffusion with a drift the heat kernel asymptotic properties are specified. Makingus e of parametrix expansion and Born approximation (instead of path integrals) we investigate semigroups generated by potential perturbations of bi-Laplacian: short-time asymptotics for the correspondingS chwartz kernel and regularized trace are derived.
Mathematics Subject Classification (2010). Primary 47D06; Secondary 35K08.
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Stepin, S.A. (2013). Short-time Asymptotics for Semigroups of Diffusion Type and Beyond. In: Kielanowski, P., Ali, S., Odzijewicz, A., Schlichenmaier, M., Voronov, T. (eds) Geometric Methods in Physics. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0448-6_38
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DOI: https://doi.org/10.1007/978-3-0348-0448-6_38
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