Damping oscillatory integrals with polynomial phase.
Decreasing Rearranged Fourier Series.
Degree of Best Approximation by Trigonometric Blending Functions.
Démonstration probabiliste de certaines inégalités de Littlewood-Paley. Exposé I : les inégalités classiques
Démonstration probabiliste de certaines inégalités de Littlewood-Paley. Exposé II : l'opérateur carré du champ
Démonstration probabiliste de certaines inégalités de Littlewood-Paley. Exposé IV : semi-groupes de convolution symétriques
Démonstration probabiliste de certaines inégalités de Littlewood-Paley. Exposé III : les inégalités générales
Density methods and results in approximation theory
Approximation theory and functional analysis share many common problems and points of contact. One of the areas of mutual interest is that of density results. In this paper we briefly survey various methods and results in this area starting from work of Weierstrass and Riesz, and extending to more recent times.
Density questions in the classical theory of moments
Let be a positive Radon measure on the real line having moments of all orders. We prove that the set of polynomials is note dense in for any , if is indeterminate. If is determinate, then is dense in for , but not necessarily for . The compact convex set of positive Radon measures with same moments as is studied in some details.
Derivatives of a Polynomial of Best Approximation.
Development in series of orthogonal polynomials with applications in optimization.
Développement asymptotique d'intégrales oscillantes lentement convergentes à l'infini
Développement en séries trigonométriques des polynômes de M. Léauté
Die Theorie der Fourier'schen Integrale und Formeln
Difference functions of periodic measurable functions
We investigate some problems of the following type: For which sets H is it true that if f is in a given class ℱ of periodic functions and the difference functions are in a given smaller class G for every h ∈ H then f itself must be in G? Denoting the class of counter-example sets by ℌ(ℱ,G), that is, , we try to characterize ℌ(ℱ,G) for some interesting classes of functions ℱ ⊃ G. We study classes of measurable functions on the circle group that are invariant for changes on null-sets (e.g. measurable...
Differentiation in lacunary directions and an extension of the Marcinkiewicz multiplier theorem
We show that the maximal operator associated to the family of rectangles in one of whose sides is parallel to for some j,k is bounded on , . We give an application of this theorem to obtain an extension of the Marcinkiewicz multiplier theorem.
Differentiation of trigonometric series
Diffraction spectra of weighted Delone sets on beta-lattices with beta a quadratic unitary Pisot number
The Fourier transform of a weighted Dirac comb of beta-integers is characterized within the framework of the theory of Distributions, in particular its pure point part which corresponds to the Bragg part of the diffraction spectrum. The corresponding intensity function on this Bragg part is computed. We deduce the diffraction spectrum of weighted Delone sets on beta-lattices in the split case for the weight, when beta is the golden mean.
Dimension and Entropy of a Non-ergodic Markovian Process and its Relation to Rademacher Riesz Products.
Disjointness results for some classes of stable processes
We discuss the disjointness of two classes of stable stochastic processes: moving averages and Fourier transforms. Results on the incompatibility of these two representations date back to Urbanik. Here we extend various disjointness results to encompass larger classes of processes.