Geodesic
On spectra of geometric operators on open manifolds and differentiable groupoids
Lauter, Robert1 ; Nistor, Victor2
1 Universität Mainz, Fachbereich 17-Mathematik, D-55099 Mainz, Germany
2 Pennsylvania State University, Department of Mathematics, University Park, PA 16802
Electronic research announcements of the American Mathematical Society, Tome 07 (2001), pp. 45-53 Cet article a éte moissonné depuis la source American Mathematical Society

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We use a pseudodifferential calculus on differentiable groupoids to obtain new analytical results on geometric operators on certain noncompact Riemannian manifolds. The first step is to establish that the geometric operators belong to a pseudodifferential calculus on an associated differentiable groupoid. This then leads to Fredholmness criteria for geometric operators on suitable noncompact manifolds, as well as to an inductive procedure to compute their essential spectra. As an application, we answer a question of Melrose on the essential spectrum of the Laplace operator on manifolds with multicylindrical ends.
DOI : 10.1090/S1079-6762-01-00093-2

Lauter, Robert 1 ; Nistor, Victor 2

1 Universität Mainz, Fachbereich 17-Mathematik, D-55099 Mainz, Germany
2 Pennsylvania State University, Department of Mathematics, University Park, PA 16802 
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Lauter, Robert; Nistor, Victor. On spectra of geometric operators on open manifolds and differentiable groupoids. Electronic research announcements of the American Mathematical Society, Tome 07 (2001), pp. 45-53. doi: 10.1090/S1079-6762-01-00093-2

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