Fourier analysis on semisimple symmetric spaces

Oshima, Toshio

doi:10.1007/bfb0090416

Cited by 10 publications

(2 citation statements)

References 8 publications

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“…Definition 1. On dit que ξ e (a q ) J est un exposant de / le long du sous-groupe parabolique P si la fonction (k, X) H-» Σ € ξ, m ( p l W /) xm n ' est P as identiquement nulle sur Brought to you by | University of Arizona Authenticated Download Date | 6/9/15 1:03 PM K* a r On appelle exposant directeur de / le long de P tout exposant de / le long de P qui est maximal pour l'ordre = defini en (16).…”

Section: Developpements Asymptotiques Et Developpements Convergentsunclassified

Terme constant des fonctions tempérées sur un espace symétrique réductif.

Carmona¹

1997

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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We define and establish the main properties of the constant term of a tempered m-spherical function F on a non riemannian Symmetrie space, finite under the action of the algebra of the G-invariant differential operators on G JH. Using the theory of asymptotics s developped in [3], [4] and [5], we extend to this case the results of [13] and [3] on the canonical decomposition of the constant term and the meromorphic dependence of the components in the case of a holomorphic family. Estimates are established which are uniform with respect to the parameter in the holomorphic case. Those results can be applied to the Eisenstein integrals studied in [10].

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Section: Developpements Asymptotiques Et Developpements Convergentsunclassified

Terme constant des fonctions tempérées sur un espace symétrique réductif.

Carmona¹

1997

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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“…Recently, considerable effort has gone into trying to understand semisimple symmetric spaces, where G is assumed semisimple. See Flensted-Jensen [2] and Oshima [9] for expositions of the current state of knowledge, which is very incomplete. The semisimple symmetric spaces possess the additional structure of an invariant semi-Riemannian metric (it is the geodesic symmetries with repect to this metric that explain the nomenclature "symmetric").…”

Section: Introductionmentioning

confidence: 99%

Harmonic Analysis on Grassmannian Bundles

Strichartz¹

1986

Transactions of the American Mathematical Society

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ABSTRACT. The harmonic analysis of the Grassmannian bundle of fc-dimensional affine subspaces of Rn, as a homogeneous space of the Euclidean motion group, is given explicitly. This is used to obtain the diagonalization of various generalizations of the Radon transform between such bundles. In abstract form, the same technique gives the Plancherel formula for any unitary representation of a semidirect product G x V (V a normal abelian subgroup) induced from an irreducible unitary representation of a subgroup of the form HxW. Introduction.Let Gn,fc denote the Grassmannian manifold of linear fc-dimensional subspaces of Rn, and let Pn>k denote the Grassmannian bundle of affine kdimensional subspaces (also called k-planes), so Pn,k is a bundle over Gn¡k with fibre dimension m, where m + k = n. In group-theoretic terms, Gn,k = G/H, where

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The Plancherel Formula on Reductive Symmetric Spaces from the Point of View of the Schwartz Space

Delorme

2005

Progress in Mathematics

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We establish the analog for real homogeneous spherical varieties of the Scattering Theorem of Sakellaridis and Venkatesh ([39], Theorem 7.3.1) for p-adic wavefront spherical varieties. We use properties of the Harish-Chandra homomorphism of Knop for invariant differential operators of the variety, special coverings of the variety and spectral projections. We have to make an analog of the Discrete Series Conjecture of Sakellaridis and Venkatesh ([39], Conjecture 9.4.6).

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Fourier analysis on semisimple symmetric spaces

Cited by 10 publications

References 8 publications

Terme constant des fonctions tempérées sur un espace symétrique réductif.

Terme constant des fonctions tempérées sur un espace symétrique réductif.

Harmonic Analysis on Grassmannian Bundles

The Plancherel Formula on Reductive Symmetric Spaces from the Point of View of the Schwartz Space

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