Pseudodifferential operators on manifolds with a Lie structure at infinity

Bernd Ammann, Robert Lauter, Victor Nistor

Research output: Contribution to journalArticlepeer-review

37 Scopus citations

Abstract

We define and study an algebra ψ1,0,ν (M0) of pseudodifferential operators canonically associated to a noncompact, Riemannian manifold M0 whose geometry at infinity is described by a Lie algebra of vector fields ν on a compactification M of M0 to a compact manifold with corners. We show that the basic properties of the usual algebra of pseudodifferential operators on a compact manifold extend to ψ1,0,ν (M0). We also consider the algebra Diff ν*(M0) of differential operators on M0 generated by ν and C (M), and show that ψ1,0,ν(M0) is a microlocalization of Diffν*(M0). Our construction solves a problem posed by Melrose in 1990. Finally, we introduce and study semi-classical and "suspended" versions of the algebra ψ1,0,ν (M0).

Original languageEnglish (US)
Pages (from-to)717-747
Number of pages31
JournalAnnals of Mathematics
Volume165
Issue number3
DOIs
StatePublished - May 2007

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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