Modulus of smoothness and theorems concerning approximation on compact groups.
Multidimensional Heisenberg convolutions and product formulas for multivariate Laguerre polynomials
Let p,q be positive integers. The groups and act on the Heisenberg group canonically as groups of automorphisms, where is the vector space of all complex p × q matrices. The associated orbit spaces may be identified with and respectively, being the cone of positive semidefinite matrices and the Weyl chamber . In this paper we compute the associated convolutions on and explicitly, depending on p. Moreover, we extend these convolutions by analytic continuation to series of convolution...
Noyau de Cauchy-Szegö d'un espace symétrique de type Cayley
Dans cet article, en utilisant les algèbres de Jordan euclidiennes, nous étudions l’espace de Hardy d’un espace symétrique de type Cayley . Nous montrons que le noyau de Cauchy-Szegö de s’exprime comme somme d’une série faisant intervenir la fonction de Harish-Chandra de l’espace symétrique riemannien , la fonction de l’espace symétrique -dual de et les fonctions sphériques de l’espace symétrique ordonné . Nous établissons, dans le cas où la dimension de l’algèbre de Jordan associée...
On a recurrence formula for elementary spherical functions on symmetric spaces and its applications to multipliers for the spherical Fourier transform.
On the Determination of Harish-Chandra's ß-Function.
On the product formula on noncompact Grassmannians
We study the absolute continuity of the convolution of two orbital measures on the symmetric space SO₀(p,q)/SO(p)×SO(q), q > p. We prove sharp conditions on X,Y ∈ for the existence of the density of the convolution measure. This measure intervenes in the product formula for the spherical functions. We show that the sharp criterion developed for SO₀(p,q)/SO(p)×SO(q) also serves for the spaces SU(p,q)/S(U(p)×U(q)) and Sp(p,q)/Sp(p)×Sp(q), q > p. We moreover apply our results to the study of...
On the singular support of distributions and Fourier transforms on symmetric spaces
On the spectra of Johnson graphs.
On unitary representations of Jacobi groups.
Paley-Wiener Type Theorems on Harmonic Extensions of H-Type Groups.
Perturbations and approximations of support functions of convex bodies.
Property (T) and groups
We show that each group in a class of finitely generated groups introduced in [2] and [3] has Kazhdan’s property (T), and calculate the exact Kazhdan constant of with respect to its natural set of generators. These are the first infinite groups shown to have property (T) without making essential use of the theory of representations of linear groups, and the first infinite groups with property (T) for which the exact Kazhdan constant has been calculated. These groups therefore provide answers...
Recurrence Formulas for Zonal Polynomials.
Reduction of invariant differential operators and expansions of conical distributions for
Relativity, spherical functions and the hypergeometric equation
Remarks on random walks on semi simple Lie groups
Représentations sphériques des groupes agissant transitivement sur un arbre semi-homogène
Selberg's trace formula on the -regular tree and applications.
Semi-groupes de Feller invariants sur les espaces hyperboliques
Some results on the unramified principal series of p-adic groups.