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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Trace expansions for elliptic cone operators with stationary domains


Authors: Juan B. Gil, Thomas Krainer and Gerardo A. Mendoza
Journal: Trans. Amer. Math. Soc. 362 (2010), 6495-6522
MSC (2010): Primary 58J35; Secondary 35P05, 47A10
Published electronically: July 20, 2010
MathSciNet review: 2678984
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Abstract: We analyze the behavior of the trace of the resolvent of an elliptic cone differential operator as the spectral parameter tends to infinity. The resolvent splits into two components, one associated with the minimal extension of the operator, and another, of finite rank, depending on the particular choice of domain. We give a full asymptotic expansion of the first component and expand the component of finite rank in the case where the domain is stationary. The results make use of, and develop further, our previous investigations on the analytic and geometric structure of the resolvent. The analysis of nonstationary domains, considerably more intricate, is pursued elsewhere.


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Additional Information

Juan B. Gil
Affiliation: Department of Mathematics, Penn State Altoona, 3000 Ivyside Park, Altoona, Pennsylvania 16601-3760

Thomas Krainer
Affiliation: Department of Mathematics, Penn State Altoona, 3000 Ivyside Park, Altoona, Pennsylvania 16601-3760

Gerardo A. Mendoza
Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05283-3
PII: S 0002-9947(2010)05283-3
Keywords: Resolvents, trace asymptotics, manifolds with conical singularities, spectral theory
Received by editor(s): November 24, 2008
Published electronically: July 20, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.