Full asymptotic expansion of the heat trace for non-self-adjoint elliptic cone operators

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Abstract

The operator e-tA and its trace Tr e-tA for t > 0, are investigated in the case when A is an elliptic differential operator on a manifold with conical singularities. Under a certain spectral condition (parameter-ellipticity) we obtain a full asymptotic expansion in t of the heat trace as t → 0+. As in the smooth compact case, the problem is reduced to the investigation of the resolvent (A - λ)-1. The main step consists in approximating this family by a parametrix of A - λ constructed within a suitable parameter-dependent calculus.

Original languageEnglish (US)
Pages (from-to)25-57
Number of pages33
JournalMathematische Nachrichten
Volume250
DOIs
StatePublished - Jan 1 2003

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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