Juan B. Gil (Temple University)
Abstract:
On smooth compact manifolds the structure of the resolvents of differential operators can be described by means of a suitable parameter-dependent pseudodifferential calculus. Moreover, resolvents can be nicely approximated within that calculus in a way that the approximation provides and asymptotic expansion in the spectral parameter. In the case of a differential equation on a region with conical points (e.g. polygons) it is natural to consider the so-called Fuchs type operators. In this talk I will briefly discuss how an adequate calculus can be used in order to analyze the resolvent structure of these operator.