Resolvents of cone pseudodifferential operators, asymptotic expansions and applications

Juan B. Gil; Paul A. Loya

doi:10.1007/s00209-007-0212-6

Resolvents of cone pseudodifferential operators, asymptotic expansions and applications

Juan B. Gil, Paul A. Loya

Division of Mathematics & Natural Sciences (Altoona)

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English (US)
Pages (from-to)	65-95
Number of pages	31
Journal	Mathematische Zeitschrift
Volume	259
Issue number	1
DOIs	https://doi.org/10.1007/s00209-007-0212-6
State	Published - May 2008

All Science Journal Classification (ASJC) codes

General Mathematics

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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.",

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AU - Loya, Paul A.

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AB - 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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U2 - 10.1007/s00209-007-0212-6

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JO - Mathematische Zeitschrift

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Resolvents of cone pseudodifferential operators, asymptotic expansions and applications

Abstract

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