Pseudo differential operators on manifolds with a Lie structure at infinity

• 成果类型: Article
• 署名作者: Ammann, Bernd; Lauter, Robert; Nistor, Victor
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2007.165.717
• 发表日期: 2007
• 页码: 717-747
• 关键词: pseudodifferential-operators; integral-operators; domains; SINGULARITIES; resolvent; propagation; SCATTERING; laplacian; groupoids; polygons

摘要

We define and study an algebra Psi(infinity)(1,0,nu)(M-0) of pseudodifferential operators canonically associated to a noncompact, Riemannian manifold M-0 whose geometry at infinity is described by a Lie algebra of vector fields V on a compactification M of M-0 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 Psi(infinity)(1,0,nu)(M-0) . We also consider the algebra Diff nu*(M-0) of differential operators on M-0 generated by nu and C infinity(M), and show that Psi(infinity)(1,0,nu)(M-0) is a microlocalization of Diff nu*(M-0). Our construction solves a prob lem posed by Melrose in 1990. Finally, we introduce and study semi-classical and suspended versions of the algebra Psi(infinity)(1,0,nu)(M-0).