The operator eβtA 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 tβ0+. As
in the smooth compact case, the problem is reduced to the investigation of the
resolvent (AβΞ»)β1. The main step will consist in approximating this
operator family by a parametrix to AβΞ» using a suitable
parameter-dependent calculus.Comment: 35 pages. Final version to appear in Math. Nachrichten. The paper has
been improved. Section 4 has been rewritten and simplifie