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In this paper, Daubechies wavelets on intervals are investigated. An analytic technique for evaluating various types of integrals containing the scaling functions is proposed; they are compared with classical techniques. Finally, these results are applied to two-point boundary value problems.

De l'analyse de Fourier à l'analyse harmonique

Jean-Paul Pier (1992)

Cahiers du séminaire d'histoire des mathématiques

Decay of Fourier transforms and summability of eigenfunction expansions

Luca Brandolini, Leonardo Colzani (2000)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Decomposition systems for function spaces

G. Kyriazis (2003)

Studia Mathematica

Let $Θ : = θ_{I}^{e} : e \in E, I \in D$ be a decomposition system for $L ₂ (ℝ^{d})$ indexed over D, the set of dyadic cubes in $ℝ^{d}$ , and a finite set E, and let $Θ ̃ : = Θ ̃_{I}^{e} : e \in E, I \in D$ be the corresponding dual functionals. That is, for every $f \in L ₂ (ℝ^{d})$ , $f = \sum_{e \in E} \sum_{I \in D} ⟨ f, Θ ̃_{I}^{e} ⟩ θ_{I}^{e}$ . We study sufficient conditions on Θ,Θ̃ so that they constitute a decomposition system for Triebel-Lizorkin and Besov spaces. Moreover, these conditions allow us to characterize the membership of a distribution f in these spaces by the size of the coefficients $⟨ f, Θ ̃_{I}^{e} ⟩$ , e ∈ E, I ∈ D. Typical examples of such decomposition systems...

Decreasing Rearranged Fourier Series.

T.W. Körner (1999)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

Degree of approximation of conjugate of a function belonging to Lip $(ξ (t), p)$ class by matrix summability means of conjugate Fourier series.

Lal, Shyam, Nigam, Hare Krishna (2001)

International Journal of Mathematics and Mathematical Sciences

Degree of Best Approximation by Trigonometric Blending Functions.

W. Haußmann, K. Jetter, B. Steinhaus (1985)

Mathematische Zeitschrift

Démonstration probabiliste de certaines inégalités de Littlewood-Paley. Exposé I : les inégalités classiques

Paul-André Meyer (1976)

Séminaire de probabilités de Strasbourg

Démonstration probabiliste de certaines inégalités de Littlewood-Paley. Exposé II : l'opérateur carré du champ

Paul-André Meyer (1976)

Séminaire de probabilités de Strasbourg

Démonstration probabiliste de certaines inégalités de Littlewood-Paley. Exposé IV : semi-groupes de convolution symétriques

Paul-André Meyer (1976)

Séminaire de probabilités de Strasbourg

Démonstration probabiliste de certaines inégalités de Littlewood-Paley. Exposé III : les inégalités générales

Paul-André Meyer (1976)

Séminaire de probabilités de Strasbourg

Denseness of the spaces $Φ_{V}$ of Lizorkin type in the mixed $L^{p ̅} (ℝ^{n})$ -spaces

Stefan Samko (1995)

Studia Mathematica

Densité de l'intégrale d'aire dans Rn+ +1 et limites non tangentielles.

Jean Brossard (1988)

Inventiones mathematicae

Densité harmonique et espaces de Banach invariants par translation ne contenant pas $c_{0}$

Myriam Déchamps (1987)

Colloquium Mathematicae

Density estimation with quadratic loss: a confidence intervals method

Pierre Alquier (2008)

ESAIM: Probability and Statistics

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

Allan Pinkus (2004)

Banach Center Publications

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.

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