Analysis of geometric operators on open manifolds: A groupoid approach

Details Analysis of geometric operators on open manifolds: A groupoid approach Analysis of geometric operators on open manifolds: A groupoid approach

2000-08-16

arxiv.org/abs/math/0008130v1

Mathematics

Spectral Theory

AMS-Latex, 43 pages

Scientific paper

We use algebras of pseudodifferential operators on groupoids to study geometric operators on non-compact manifolds and singular spaces. The first step is to establish that the geometric operators are in our algebras. This then leads to criteria for Fredholmness for geometric operators on suitable non-compact manifolds, as well as to an inductive procedure to study their essential spectrum. As an application, we answer a question of Melrose on the essential spectrum of the Laplace operator on manifolds with multi-cylindrical ends.

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