✦ LIBER ✦
Full asymptotic expansion of the heat trace for non–self–adjoint elliptic cone operators
✍ Scribed by Juan B. Gil
- Publisher
- John Wiley and Sons
- Year
- 2003
- Tongue
- English
- Weight
- 458 KB
- Volume
- 250
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
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.