Program WHAT 7-8 July 2008

WHAT, Orléans, 7-8 July 2008

Tentative program

Talks in the Science Building (amphi S, ground floor)
Breaks in the Mathematics Building (cafeteria, ground floor)

Wednesday July 9
07:15 : bus departure to Orsay (meeting point behind the cathedral in Orléans).

Lectures

Piero D'ANCONA (Università La Sapienza - Roma 1) : Smoothing phenomena for equations with variable coefficients

Adam KORÁNYI (CUNY) : Cartan-Helgason theorem, Poisson transform, and Satake-Furstenberg compactifications
Abstract : The Cartan-Helgason theorem (a representation of a semisimple G on a finite dimensional V has a spherical vector e if and only if it has a conical vector v) has a two-line proof based on the Fatou-type theorem of the Poisson transform. The basic fact is that the orbit of e on the projectivized V is a copy of the symmetric space G/K, while the orbit of v, which now lies on the topological boundary of G/K, is a Poisson boundary of G/K. This observation leads to a construction of the Satake-Furstenberg compactifications of G/K which seems to be the simplest of all the existing constructions.

Communications

Chokri ABDELKEFI and Feriel SASSI (IPEI Tunis) : Characterizations of Besov-type spaces associated to the Dunkl operators and Dunkl transform

Włodzimierz BĄK (Uniwersytet Opolski) : About some generalization of the Lyons-Sullivans construction
Abstract : A modification of the Lyons-Sullivan discretization of positive harmonic functions on a Riemannian manifold M is proposed. This modification, depending on a choice of constants C={C_n|n=1,2,...}, allows for constructing measures ν_C,x, x∈M, supported on a discrete subset Γ of M, such that, for every positive harmonic function f on M, f(x)= ∑_γ∈Γ f(γ) ν_C,x(γ). For different choices of the sequences C the measures ν_C,x are essentially different (e.g. they may have different moments). Furthermore the family of measures ν_C,x is convex when the sequence C varies.

Néjib BEN SALEM (Faculté des Sciences de Tunis) : Pizzetti series and polyharmonicity associated with the Dunkl-Laplacian

Latifa BOUATTOUR (Faculté des Sciences de Tunis) : Théorème de Beurling-Hörmander sur les groupes de Lie semi-simples

Samir KALLEL (ISIMM, Monastir) : Bessel and Flett potentials associated with Dunkl operators on R^d

Emilie DAVID-GUILLOU (Université du Luxembourg) : Kernel theorem on solvable Lie groups
Abstract : In this talk, I will present the construction of a set S of smooth functions with rapid decay on certain class of solvable Lie groups. These groups have in particular exponential growth of the volume, and we will see what "rapid decay" means in this setting. I will then show that for this class of groups, every linear operator bounded from L^p to L^q and invariant by translations, has a unique convolution kernel in the dual space of the space S. We will see that this last result is a corollary of a kernel theorem of type Schwartz for the functions in S.

Lotfi KAMOUN (Faculté des Sciences de Monastir) : Lipschitz spaces associated with the reflection group Z₂^d

Małgorzata LETACHOWICZ (Uniwersytet Wrocławski) : On spectral l ¹ multipliers for convolution operators on periodic solvable groups

Tao MEI (University of Illinois at Urbana-Champaign) : A weak (1,1) inequality for matrix(operator)-valued Littlewood-Paley G-function
Abstract : We consider n by n matrix-valued function f for large n and the corresponding G-function G(f) = ( ∫₀^∞ |∇f(x,t)|² t dt )^1/2 . Here f(x,t) is the Poisson integral of f at (x,t), ∇ is the usual gradient to each coefficient of the matrix-valued function f(x,t) and |a| means (a*a)^1/2 for matrices a. We study weak (1,1) inequality for G(f) and wish a constant independent of n. We will show how the situation is different from the scalar-valued case. This is a recent joint work with Javier Parcet.

Mohamed Ali MOUROU (INSAT Tunis) : Formule reproduisante de Calderon associée à l'opérateur de Dunkl sur R

Short presentations

Fatma AYADI (Faculté des Sciences de Tunis & Université d'Orléans) : The Schrödinger and the wave equation associated to the Dunkl-Cherednik laplacian

Seifallah GHOBBER (Faculté des Sciences de Tunis & Université d'Orléans) : Principe d'incertitude de Heisenberg sur les groupes finis