Estimations de la fonction maximale de Hardy-Littlewood
On montre que la fonction maximale de Hardy-Littlewood est de type sur certains groupes de Lie et variétés de Cartan-Hadamard.
Flensted-Jensen's functions attached to the Landau problem on the hyperbolic disc
We give an explicit expression of a two-parameter family of Flensted-Jensen’s functions on a concrete realization of the universal covering group of . We prove that these functions are, up to a phase factor, radial eigenfunctions of the Landau Hamiltonian on the hyperbolic disc with a magnetic field strength proportional to , and corresponding to the eigenvalue .
Fonctions généralisées sphériques sur
Fonctions sphériques associées à une mesure bornée, hermitienne et idempotente
Fonctions sphériques et opérateurs de Hecke
Functional Equation for Spherical Functions on Finite Groups.
Gelfand pairs and spherical functions.
Generalisations of some properties of invariant polynomials with matrix arguments
Some extensions of the properties of invariant polynomials proved by Davis (1980), Chikuse (1980), Chikuse and Davis (1986) and Ratnarajah et al. (2005) are given for symmetric and Hermitian matrices.
Generalized Gelfand pairs associated with the Heisenberg group. (Paires de Guelfand généralisées associées au groupe d'Heisenberg.)
Harmonic analysis and Radon transforms on pencils of geodesics.
Harmonic analysis for spinors on real hyperbolic spaces
We develop the L² harmonic analysis for (Dirac) spinors on the real hyperbolic space Hⁿ(ℝ) and give the analogue of the classical notions and results known for functions and differential forms: we investigate the Poisson transform, spherical function theory, spherical Fourier transform and Fourier transform. Very explicit expressions and statements are obtained by reduction to Jacobi analysis on L²(ℝ). As applications, we describe the exact spectrum of the Dirac operator, study the Abel transform...
Harmonic Analysis for Vector Fields on Hyperbolic Spaces.
Harmonic analysis of spherical functions on
Denote by the algebra of spherical integrable functions on , with convolution as multiplication. This is a commutative semi-simple algebra, and we use its Gelfand transform to study the ideals in . In particular, we are interested in conditions on an ideal that ensure that it is all of , or that it is . Spherical functions on are naturally represented as radial functions on the unit disk in the complex plane. Using this representation, these results are applied to characterize harmonic...
Harmonic Analysis on Real Reductive Groups. II.
Invariant analysis and contractions of symmetric spaces : part II
Invariant operators on function spaces on homogeneous trees
Inversion de la transformation de Pompéiu dans le disque hyperbolique (Cas de deux disques).
In this paper we extend the result established for the euclidean space in [3] to the hyperbolic disk. This includes the reconstruction of a function defined in a fixed disk B(0,R) from its averages on disks of radii r1, r2 lying in B(0, R).
Jordan algebras and generalized principle series representations.
-estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. II.
Macdonald formula for spherical functions on affine buildings
In this paper we explicitly determine the Macdonald formula for spherical functions on any locally finite, regular and affine Bruhat-Tits building, by constructing the finite difference equations that must be satisfied and explaining how they arise, by only using the geometric properties of the building.