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
Denseness of the spaces of Lizorkin type in the mixed -spaces
Densité de l'intégrale d'aire dans Rn+ +1 et limites non tangentielles.
Densité harmonique et espaces de Banach invariants par translation ne contenant pas
Density estimation with quadratic loss: a confidence intervals method
We propose a feature selection method for density estimation with quadratic loss. This method relies on the study of unidimensional approximation models and on the definition of confidence regions for the density thanks to these models. It is quite general and includes cases of interest like detection of relevant wavelets coefficients or selection of support vectors in SVM. In the general case, we prove that every selected feature actually improves the performance of the estimator. In the case...
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.
Describing Functions: Atomic Decompositions Versus Frames.
Designing Multiresolution Analysis-type Wavelets and Their Fast Algorithms.
Determination of the number of texture segments using wavelets.
Development in series of orthogonal polynomials with applications in optimization.
Developments from nonharmonic Fourier series.
Développement asymptotique d'intégrales oscillantes lentement convergentes à l'infini
Développement en séries trigonométriques des polynômes de M. Léauté
Diagonals of Self-adjoint Operators with Finite Spectrum
Given a finite set X⊆ ℝ we characterize the diagonals of self-adjoint operators with spectrum X. Our result extends the Schur-Horn theorem from a finite-dimensional setting to an infinite-dimensional Hilbert space analogous to Kadison's theorem for orthogonal projections (2002) and the second author's result for operators with three-point spectrum (2013).
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...
Differentiability of distributions at a single point