The Wiener Property for a Class of Discrete Hypergroups.
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.
The Witt group of quadratic characters.
Théorème central limite local sur certains groupes de Lie
Théorème central limite sur les groupes nilpotents
Théorème de Fatou pour les fonctions propres des opérateurs différentiels invariants par un groupe de déplacements de Cartan
Nous étudions le comportement à l’infini des intégrales de Poisson liées aux groupes de déplacements de Cartan.
Theorems on lacunary sets, especially p-Sidon sets
Théorie de Littlewood-Paley-Stein et processus stables
Theta Functions and Symplectic Groups.
Thickness conditions and Littlewood-Paley sets
We consider sets in the real line that have Littlewood-Paley properties LP(p) or LP and study the following question: How thick can these sets be?
Thickness in topological transformation semigroups.
Thin sets defined by a sequence of continuous functions
Thin sets in nonlinear potential theory
Let , denote the space of Bessel potentials , , with norm . For integer can be identified with the Sobolev space .One can associate a potential theory to these spaces much in the same way as classical potential theory is associated to the space , and a considerable part of the theory was carried over to this more general context around 1970. There were difficulties extending the theory of thin sets, however. By means of a new inequality, which characterizes the positive cone in the space...
Thin sets in trigonometrical series and quasinormal convergence
Three results in Dunkl analysis
We first establish a geometric Paley-Wiener theorem for the Dunkl transform in the crystallographic case. Next we obtain an optimal bound for the norm of Dunkl translations in dimension 1. Finally, we describe more precisely the support of the distribution associated to Dunkl translations in higher dimension.
Three results on I-sets
Three-dimensional reconstruction from projections
Computerized tomograhphy is a technique for computation and visualization of density (i.e. X- or -ray absorption coefficients) distribution over a cross-sectional anatomic plane from a set of projections. Three-dimensional reconstruction may be obtained by using a system of parallel planes. For the reconstruction of the transverse section it is necessary to choose an appropriate method taking into account the geometry of the data collection, the noise in projection data, the amount of data, the...
Time Dependent Perturbations and Scattering of Strongly Continuous Groups on Banach Spaces.
Topics on Kronecker sets
We obtain three theorems about transformation of sets of multiplicity onto Kronecker sets, by means of functions of various differentiability classes. The same method yields an improved theorem on the union of two Kronecker sets.
Topological and geometrical properties of mappings with summable Jacobian in Sobolev classes. I.