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

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.