Titlebook: Noncommutative Harmonic Analysis; In Honor of Jacques Patrick Delorme,Michèle Vergne Book 2004 Birkhäuser Boston 2004 Dolbeault cohomology

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,Symmetric spaces and star representations III. The Poincaré disc,s. We realize the regularrepresentation of .(2, ℝ) on the space of smooth functions on the Poincare disc as a subrepresentation of .(2, ℝ) in the Weyl–Moyal star product algebra on ℝ.. We indicate how it is possible to extend our construction to the general case of a Hermitian symmetric space of tub

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Local zeta functions for a class of symmetric spaces,ily of symmetric spaces arising from 3-gradings of reductive Lie algebras. Let . be a 3-graded real reductive Lie algebra. Let . be the adjoint group of . and let . be the analytic subgroup of . corresponding to the Lie algebra g. We make the assumption that the prehomogeneous vector space (., ... i

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,La formule de Plancherel pour les groupes de Lie presque algébriques réels, a proof of this formula in the philosophy of the orbit method and following the lines of the one given by M. Duflo and M. Vergne for simply connected semisimple Lie groups..The main ingredients of the proof are:.In order to illustrate the main steps of the proof, we treat the example of the semidir

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,Representations of ,, and the distribution of points in ℙ,,inal problem is the following: Let . = .(..,..,..., ..) be the function field of affine .-space . = .. over an algebraically closed field ., and suppose . ⊂ . is any subfield. Then the question is: Is . = . ∩ .[..,..,..., .] a finitely generated .-algebra. In most cases of interest, . is the field o

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A localization argument for characters of reductive Lie groups: an introduction and examples,tirely different character formulas for reductive Lie groups and answers the question posed in [Sch]..A corresponding problem in the compact group setting was solved by N. Berline, E. Getzler and M. Vergne in [BGV] by an application of the theory of equivariant forms and, particularly, the fixed poi

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Summation formulas, from Poisson and Voronoi to the present,on of Poisson summation asserts the equality. valid (at least) for all Schwartz functions .. Let us take a brief historical detour to the beginning of the 20th century, before the notion of Schwartz function had been introduced. The custom then was to state (1.1) for more general functions .,such as