Vol. 4, No. 1, 2011

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ISSN: 1948-206X (e-only)
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Dynamics on Grassmannians and resolvents of cone operators

Juan B. Gil, Thomas Krainer and Gerardo A. Mendoza

Vol. 4 (2011), No. 1, 115–148
Abstract

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
Mathematical Subject Classification 2010
Primary: 58J35
Secondary: 37C70, 35P05, 47A10
Milestones
Received: 30 June 2009
Revised: 10 March 2010
Accepted: 11 June 2010
Published: 27 March 2011
Authors
Juan B. Gil
Department of Mathematics
Penn State Altoona
3000 Ivyside Park
Altoona, PA 16601
United States
Thomas Krainer
Department of Mathematics
Penn State Altoona
3000 Ivyside Park
Altoona, PA 16601
United States
Gerardo A. Mendoza
Department of Mathematics
Temple University
Philadelphia, PA 19122
United States