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

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Summation formulas, from Poisson and Voronoi to the present,ndeed, the general case of (1.2) can be reduced to the special case of . = 0, . = 1, which amounts to the statement that the Fourier series of a periodic function of bounded variation converges pointwise, to the average of its left and right-hand limits.
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0743-1643 s as a powerful tool.This volume is devoted to the theme of Noncommutative Harmonic Analysis and consists of articles in honor of Jacques Carmona, whose scientific interests range through all aspects of Lie group representations. The topics encompass the theory of representations of reductive Lie gr
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,La formule de Plancherel pour les groupes de Lie presque algébriques réels, 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 semidirect product of the universal covering of SL.(ℝ) by the three-dimensional Heisenberg group.
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Intertwining ladder representations for SU(,, ,) into Dolbeault cohomology,es the Dolbeault model into the vector bundle model. By passing through the Fock space realization of the ladder representations, we invert the Penrose transform, and thus intertwine the ladder representations into Dolbeault cohomology.
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,McKay’s correspondence and characters of finite subgroups of ,(2),aturally as numerators of Poincaré series associated to finite subgroups of SU(2) acting on polynomials in two variables. These polynomials have been the subject of a number of investigations, but their interpretation as characters has apparently not been noticed.
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