%0 Journal Article
%T Asymptotic and exact expansions of heat traces
%A Micha£¿ Eckstein
%A Artur Zaj£¿c
%J Mathematics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1412.5100v1