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

Abstract

The operator $e^{-tA}$ and its trace are investigated in the case when $A$ is a non-self-adjoint 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 $t\to 0^{+}$. As in the smooth compact case, the problem is reduced to the investigation of the resolvent $(A-\lambda {)}^{-1}$. The main step will consist in approximating this operator family by a parametrix to $A-\lambda$ using a suitable parameter-dependent calculus.

35 pages. Final version to appear in Math. Nachrichten. The paper has been improved. Section 4 has been rewritten and simplified

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