Mathematische Zeitschrift

, Volume 259, Issue 1, pp 65–95

Resolvents of cone pseudodifferential operators, asymptotic expansions and applications

Article

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.

Keywords

Pseudodifferential operators Manifolds with conical singularities Resolvents Heat kernels Zeta functions Analytic index formulas 

Mathematics Subject Classification (2000)

Primary 58J35 Secondary 58J40 58J37 58J20 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Penn State AltoonaAltoonaUSA
  2. 2.Department of MathematicsBinghamton UniversityBinghamtonUSA

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