Mathematische Zeitschrift

, Volume 259, Issue 1, pp 65–95

Resolvents of cone pseudodifferential operators, asymptotic expansions and applications


DOI: 10.1007/s00209-007-0212-6

Cite this article as:
Gil, J.B. & Loya, P.A. Math. Z. (2008) 259: 65. doi:10.1007/s00209-007-0212-6


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.


Pseudodifferential operatorsManifolds with conical singularitiesResolventsHeat kernelsZeta functionsAnalytic index formulas

Mathematics Subject Classification (2000)

Primary 58J35Secondary 58J4058J3758J20

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

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