6533b833fe1ef96bd129c03a
RESEARCH PRODUCT
On spectra of geometric operators on open manifolds and differentiable groupoids
Victor NistorRobert Lautersubject
Discrete mathematicsPure mathematicsHigher-dimensional algebraMathematics::Operator AlgebrasGeneral MathematicsEssential spectrumMathematics::Spectral TheoryOperator theoryCompact operatorQuasinormal operatorMathematics::K-Theory and HomologyDouble groupoidMathematics::Differential GeometryDifferentiable functionMathematics::Symplectic GeometryLaplace operatorMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2001-05-08 | Electronic Research Announcements of the American Mathematical Society |