Resolvents of cone pseudodifferential operators, asymptotic expansions and applications

Details Resolvents of cone pseudodifferential operators, asymptotic expansions and applications Resolvents of cone pseudodifferential operators, asymptotic expansions and applications

2006-04-14

arxiv.org/abs/math/0604338v1

Mathematics

Spectral Theory

30 pages, 5 figures

Scientific paper

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.

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