The paper proves the existence and elucidates the structure of the asymptotic
expansion of the trace of the resolvent of a closed extension of a general elliptic cone
operator on a compact manifold with boundary as the spectral parameter tends to
infinity. The hypotheses involve only minimal conditions on the symbols of the
operator. The results combine previous investigations by the authors on the subject
with an analysis of the asymptotics of a family of projections related to the domain.
This entails a detailed study of the dynamics of a flow on the Grassmannian of
domains.
Keywords
resolvents, trace asymptotics, manifolds with conical
singularities, spectral theory, dynamics on Grassmannians