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.