Mathematische Zeitschrift

, Volume 259, Issue 1, pp 65–95

Resolvents of cone pseudodifferential operators, asymptotic expansions and applications


    • Penn State Altoona
  • Paul A. Loya
    • Department of MathematicsBinghamton University

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 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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© Springer-Verlag 2007