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Dynamics on
Grassmannians and resolvents of cone operators
Juan B. Gil, Thomas Krainer and Gerardo A. Mendoza |
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Vol. 4 (2011), No. 1, 115–148
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Abstract |
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The paper proves the existence and elucidates the structure of the asymptotic expansion of the trace of the resolvent of a closed extension of a general elliptic cone operator on a compact manifold with boundary as the spectral parameter tends to infinity. The hypotheses involve only minimal conditions on the symbols of the operator. The results combine previous investigations by the authors on the subject with an analysis of the asymptotics of a family of projections related to the domain. This entails a detailed study of the dynamics of a flow on the Grassmannian of domains. |
Keywords
resolvents, trace asymptotics, manifolds with conical
singularities, spectral theory, dynamics on Grassmannians
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Mathematical Subject Classification 2010
Primary: 58J35
Secondary: 37C70, 35P05, 47A10
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Milestones
Received: 30 June 2009
Revised: 10 March 2010
Accepted: 11 June 2010
Published: 27 March 2011
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Authors |
| Juan B. Gil | |
| Department of Mathematics Penn State Altoona 3000 Ivyside Park Altoona, PA 16601 United States |
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| Thomas Krainer | |
| Department of Mathematics Penn State Altoona 3000 Ivyside Park Altoona, PA 16601 United States |
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| Gerardo A. Mendoza | |
| Department of Mathematics Temple University Philadelphia, PA 19122 United States |
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