Terme constant des fonctions tempérées sur un espace symétrique réductif.
The asymptotics of spherical functions and the central limit theorem on symmetric cones
We prove a central limit theorem for certain invariant random variables on the symmetric cone in a formally real Jordan algebra. This extends form the previous results of Richards and Terras on the cone of real positive definite matrices.
The determination of convex bodies from the size and shape of their projections and sections
We survey results concerning the extent to which information about a convex body's projections or sections determine that body. We will see that, if the body is known to be centrally symmetric, then it is determined by the size of its projections. However, without the symmetry condition, knowledge of the average shape of projections or sections often determines the body. Rather surprisingly, the dimension of the projections or sections plays a key role and exceptional cases do occur but appear to...
The Fourier Transform of Harish-Chandra's c-Function and Inversion of the Able Transform.
The infinite Brownian loop on a symmetric space.
The irreducible unitary -spherical representations of
The Poisson equation in homogeneous Sobolev spaces.
The Poisson Transform for Split Reductive Symmetric Spaces.
The product formula for the spherical functions on symmetric spaces of noncompact type.
The spherical transform for homogeneous vector bundles over Riemannian symmetric spaces.
The Stanley-Féray-Śniady formula for the generalized characters of the symmetric group
We show that the explicit formula of Stanley-Féray-Śniady for the characters of the symmetric group has a natural extension to the generalized characters. These are the spherical functions of the unbalanced Gel’fand pair .
The Wigner semi-circle law and the Heisenberg group
The Wigner Theorem states that the statistical distribution of the eigenvalues of a random Hermitian matrix converges to the semi-circular law as the dimension goes to infinity. It is possible to establish this result by using harmonic analysis on the Heisenberg group. In fact this convergence corresponds to the topology of the set of spherical functions associated to the action of the unitary group on the Heisenberg group.
Transformation de Fourier sphérique de type