Resolvents of cone pseudodifferential operators, asymptotic expansions and applications

Abstract

We study the structure and asymptotic behavior of the resolvent of elliptic cone pseudodifferential operators acting on weighted Sobolev spaces over a compact manifold with boundary. We obtain an asymptotic expansion of the resolvent as the spectral parameter tends to infinity, and use it to derive corresponding heat trace and zeta function expansions as well as an analytic index formula.

30 pages, 5 figures

References in corpus (2)

• On the resolvent and spectral functions of a second order differential operator with a regular singularity
• Unusual poles of the $\zeta$-functions for some regular singular differential operators