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

The operator $e^{-tA}$ and its trace are investigated in the case when $A$ is\na non-self-adjoint elliptic differential operator on a manifold with conical\nsingularities. Under a certain spectral condition (parameter-ellipticity) we\nobtain a full asymptotic expansion in $t$ of the heat trace as $t\\to 0^+$. As\nin the smooth compact case, the problem is reduced to the investigation of the\nresolvent $(A-\\lambda)^{-1}$. The main step will consist in approximating this\noperator family by a parametrix to $A-\\lambda$ using a suitable\nparameter-dependent calculus.\n