A survey on the Weierstrass approximation theorem.
Algèbres -adiques
An Algebraic Approach to Discrete Dilations. Application to Discrete Wavelet Transforms.
An Inversion Formula for the Radon Transform on Trees.
An Lp − Lq - Version of Morgan's Theorem Associated with Partial Differential Operators
2000 Mathematics Subject Classification: 42B10, 43A32.In this paper we take the strip KL = [0, +∞[×[−Lπ, Lπ], where L is a positive integer. We consider, for a nonnegative real number α, two partial differential operators D and Dα on ]0, +∞[×] − Lπ, Lπ[. We associate a generalized Fourier transform Fα to the operators D and Dα. For this transform Fα, we establish an Lp − Lq − version of the Morgan's theorem under the assumption 1 ≤ p, q ≤ +∞.
Asymptotic behaviour of generalized Poisson integrals in rank one symmetric spaces and in trees
Beurling-Figà-Talamanca-Herz algebras
For a locally compact group G and p ∈ (1,∞), we define and study the Beurling-Figà-Talamanca-Herz algebras . For p = 2 and abelian G, these are precisely the Beurling algebras on the dual group Ĝ. For p = 2 and compact G, our approach subsumes an earlier one by H. H. Lee and E. Samei. The key to our approach is not to define Beurling algebras through weights, i.e., possibly unbounded continuous functions, but rather through their inverses, which are bounded continuous functions. We prove that...
Beurling-Hörmander uncertainty principle for the spherical mean operator.
Compact simple Lie groups and their -, -, and -transforms.
Continuous wavelet transform on semisimple Lie groups and inversion of the Abel transform and its dual.
In this work we define and study wavelets and continuous wavelet transform on semisimple Lie groups G of real rank l. We prove for this transform Plancherel and inversion formulas. Next using the Abel transform A on G and its dual A*, we give relations between the continuous wavelet transform on G and the classical continuous wavelet transform on Rl, and we deduce the formulas which give the inverse operators of the operators A and A*.
Corrections à: «Transformations de Fourier et majoration de sommes exponentielles»
Decomposition of analytic measures on groups and measure spaces
We consider an arbitrary locally compact abelian group G, with an ordered dual group Γ, acting on a space of measures. Under suitable conditions, we define the notion of analytic measures using the representation of G and the order on Γ. Our goal is to study analytic measures by applying a new transference principle for subspaces of measures, along with results from probability and Littlewood-Paley theory. As a consequence, we derive new properties of analytic measures as well as extensions of previous...
Dirac operators, conformal transformations and aspects of classical harmonic analysis.
Discrete marginal problem for complex measures
Domains of Integral Transformations on General Measure Spaces.
Dual algebras.
Dunkl translation and uncentered maximal operator on the real line.
Dunkl-Gabor transform and time-frequency concentration
The aim of this paper is to prove two new uncertainty principles for the Dunkl-Gabor transform. The first of these results is a new version of Heisenberg’s uncertainty inequality which states that the Dunkl-Gabor transform of a nonzero function with respect to a nonzero radial window function cannot be time and frequency concentrated around zero. The second result is an analogue of Benedicks’ uncertainty principle which states that the Dunkl-Gabor transform of a nonzero function with respect to...
Fourier Transforms of Schwartz Functions on Chébli-Trimèche Hypergroups.
Hardy and Cowling-Price theorems for a Cherednik type operator on the real line
This paper is aimed to establish Hardy and Cowling-Price type theorems for the Fourier transform tied to a generalized Cherednik operator on the real line.