相关论文: Pseudodifferential operators on differential group…
On filtered manifolds one can define a different notion of order for the differential operators. In this paper, we use generalized fixed point algebras to construct a pseudodifferential extension that reflects this behaviour. In the…
The Lie algebra of pseudodifferential symbols on the circle has a nontrivial central extension (by the ``logarithmic'' 2-cocycle) generalizing the Virasoro algebra. The corresponding extended subalgebra of integral operators generates the…
We build a longitudinally smooth differentiable groupoid associated to any manifold with corners. The pseudodifferential calculus on this groupoid coincides with the pseudodifferential calculus of Melrose (also called b-calculus). We also…
Classical pseudo-differential operators of order zero on a graded nilpotent Lie group $G$ form a $^*$-subalgebra of the bounded operators on $L^2(G)$. We show that its $C^*$-closure is an extension of a noncommutative algebra of principal…
In this paper, we define in an intrinsic way operators on a compact Lie group by means of symbols using the representations of the group. The main purpose is to show that these operators form a symbolic pseudo-differential calculus which…
The goal of this paper is to construct a calculus whose higher indices are naturally elements in the twisted K-theory groups for Lie groupoids. Given a Lie groupoid $G$ and a $PU(H)$-valued groupoid cocycle, we construct an algebra of…
We introduce a Lie bialgebra structure on the central extension of the Lie algebra of differential operators on the line and the circle (with scalar or matrix coefficients). This defines a Poisson--Lie structure on the dual group of…
We construct algebras of pseudodifferential operators on a continuous family groupoid G that are closed under holomorphic functional calculus, contain the algebra of all pseudodifferential operators of order 0 on G as a dense subalgebra,…
We prove a general black box result which produces algebras of pseudodifferential operators (ps.d.o.s) on noncompact manifolds, together with a precise principal symbol calculus. Our construction (which also applies in parameter-dependent…
In this paper, we present first results of our investigation regarding symbolic pseudo-differential calculi on nilpotent Lie groups. On any graded Lie group, we define classes of symbols using difference operators. The operators are…
Associated to a Lie groupoid, there are two $C^*$-algebras: the full and the reduced one. The associated order $0$ pseudodifferential calculus gives rise to multiplier algebras of both. We prove that both associated corona algebras are…
We extend the Ruzhansky-Turunen theory of pseudo differential operators on compact Lie groups into a tool that can be used to investigate group-valued Markov processes in the spirit of the work in Euclidean spaces of N.Jacob and…
We consider a smooth hyper-surface Z of a closed Riemannian manifold X. Let P be the Poisson operator associating to a smooth function on Z its harmonic extension on X\Z. If A is a pseudo-differential operator on X of degree <3, we prove…
A generalization of differential operators are pseudodifferential operators which are used for reasoning about partial differential equations with variable coefficients. A lot of useful properties about classical pseudodifferential…
Related to a semigroup of operators on a metric measure space, we define and study pseudodifferential operators (including the setting of Riemannian manifold, fractals, graphs ...). Boundedness on $L^p$ for pseudodifferential operators of…
We search for pseudo-differential operators acting on holomorphic Sobolev spaces. The operators should mirror the standard Sobolev mapping property in the holomorphic analogues. The setting is a closed real-analytic Riemannian manifold, or…
This paper provides a toolbox of para-differential calculus on compact Lie groups. The toolbox is based on representation theory of compact Lie groups and contains exact formulas of symbolic calculus. Para-differential operators are…
We study a large class of Poisson manifolds, derived from Manin triples, for which we construct explicit partitions into regular Poisson submanifolds by intersecting certain group orbits. Examples include all varieties ${\mathcal L}$ of…
The aim of this work is to develop a global calculus for pseudo-differential operators acting on suitable algebras of generalized functions. In particular, a condition of global hypoellipticity of the symbols gives a result of regularity…
The importance of the theory of pseudo-differential operators in the study of non linear integrable systems is point out. Principally, the algebra $\Xi $ of nonlinear (local and nonlocal) differential operators, acting on the ring of…