6533b826fe1ef96bd1283b36

RESEARCH PRODUCT

Analysis of geometric operators on open manifolds: A groupoid approach

Victor NistorRobert Lauter

subject

Pure mathematicsSpectral theoryMathematics::Operator Algebras010102 general mathematicsMathematical analysisSpectral geometryFinite-rank operatorOperator theoryCompact operator01 natural sciencesQuasinormal operatorSemi-elliptic operatorElliptic operatorMathematics::K-Theory and Homology0103 physical sciences010307 mathematical physics0101 mathematicsMathematics::Symplectic GeometryMathematics

description

The first five sections of this paper are a survey of algebras of pseudodifferential operators on groupoids. We thus review differentiable groupoids, the definition of pseudodifferential operators on groupoids, and some of their properties. We use then this background material to establish a few new results on these algebras, results that are useful for the analysis of geometric operators on non-compact manifolds and singular spaces. The first step is to establish that the geometric operators on groupoids are in our algebras. This then leads to criteria for the Fredholmness of geometric operators on suitable non-compact manifolds, as well as to an inductive procedure to study their essential spectra. As an application, we answer a question of Melrose on the essential spectrum of the Laplace operator on manifolds with multi-cylindrical ends.

yearjournalcountryeditionlanguage
2001-01-01
https://doi.org/10.1007/978-3-0348-8364-1_8