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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 construction
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 is
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 for
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 on
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 of
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 of
Improving the rate of convergence of ‘high order finite elements’ on polygons and domains with cusps
This paper provides 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 �’ and not on n (the authors do not assume u ∉ Hm+1( ℙ).
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 a
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 of
On the geometry of Riemannian manifolds with a Lie structure at infinity
A generalization of the geodesic spray is studied and conditions for noncomapct manifolds with a Lie structure at infinity to have positive injectivity radius are given and it is proved that the geometric operators are generated by the given Lie algebra of vector fields.