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

The operator e(-tA) and its trace Tre(-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-lambda)(-1). The main step consists in approximating this family by a parametrix of A-lambda constructed within a suitable parameter-dependent calculus.