Asymptotic and exact expansions of heat traces

Bibliographic description

punktacja MEiN [2015 A]: 25

title:	Asymptotic and exact expansions of heat traces
author:	Eckstein Michał , Zając Artur
journal title:	Mathematical Physics, Analysis and Geometry
volume:	18
issue:	1
date of publication :	2015
article ID:	28
ISSN:	1385-0172
eISSN:	1572-9656
DOI:	10.1007/s11040-015-9197-2
language:	English
journal language:	English
abstract in English:	We study heat traces associated with positive unbounded operators with compact inverses. With the help of the inverse Mellin transform we derive necessary conditions for the existence of a short time asymptotic expansion. The conditions are formulated in terms of the meromorphic extension of the associated spectral zeta-functions and proven to be verified for a large class of operators. We also address the problem of convergence of the obtained asymptotic expansions. General results are illustrated with a number of explicit examples.
keywords in English:	heat traces, asymptotic expansions, spectral theory, zeta-functions, general Dirichlet series
number of pulisher's sheets:	2,9
affiliation:	Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego, Wydział Matematyki i Informatyki
type:	journal article
subtype:	academic paper