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Pseudodifferential operators on differential groupoids
We construct an algebra of pseudodifferential operators on each groupoid in a class that generalizes differentiable groupoids to allow manifolds with corners. We show that this constructionExpand
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Group cohomology and the cyclic cohomology of crossed products
Definite results are obtained in the conditions: the group G is torsion free and the class ~h of the extension 0 ~ Zh ~ G h --* N h --+ 0 in H2(Nh, ) @ k is niipotent (here Gh, for h~ G, stands forExpand
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Homology of pseudodifferential operators I. Manifolds with boundary
The Hochschild and cyclic homology groups are computed for the algebra of `cusp' pseudodifferential operators on any compact manifold with boundary. The index functional for this algebra isExpand
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Analysis of geometric operators on open manifolds: A groupoid approach
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 onExpand
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Pseudodifferential Analysis on Continuous Family Groupoids
We study properties and representations of the convo- lution algebra and the algebra of pseudodieren tial operators asso- ciated to a continuous family groupoid. We show that the study ofExpand
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Interface and mixed boundary value problems on n-dimensional polyhedral domains
Let � 2 Z+ be arbitrary. We prove a well-posedness result for mixed boundary value/interface problems of second-order, positive, strongly elliptic operators in weighted Sobolev spaces K �() on aExpand
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Pseudodifferential operators on manifolds with a Lie structure at infinity
We define and study an algebra Ψ ∞,0,V (M0) of pseudodifferential operators canonically associated to a noncompact, Riemannian manifold M0 whose geometry at infinity is described by a Lie algebra ofExpand
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On the geometry of Riemannian manifolds with a Lie structure at infinity
TLDR
We study a generalization of the geodesic spray and give conditions for noncomapct manifolds with a Lie structure at infinity to have positive injectivity radius. Expand
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Improving the rate of convergence of ‘high order finite elements’ on polygons and domains with cusps
TLDR
We provide a construction of a new sequence of finite dimensional subspaces Vn such that where f ∈ Hm−1(ℙ) is arbitrary and C is a constant that depends only on ℙ and not on n. Expand
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GROUPOIDS AND THE INTEGRATION OF LIE ALGEBROIDS
We show that a Lie algebroid on a stratified manifold is integrable if, and only if, its restriction to each strata is integrable. These results allow us to construct a large class of algebras ofExpand
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