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Entrelacement de co-Poisson

Jean-François Burnol (2007)

Annales de l’institut Fourier

On connaît le lien intime qui existe entre les équations fonctionnelles des fonctions L et les formules sommatoires dont le prototype est donné par celle de Poisson. Ce lien fait intervenir la transformation intégrale de Fourier et ses généralisations. Ici, nous réexaminons la signification harmonique (ainsi qu’hilbertienne et distributionnelle) des équations fonctionnelles ayant la forme la plus simple, à savoir, celle s’appliquant pour la fonction dzêta de Riemann et les séries L de Dirichlet...

Entropic approximation in kinetic theory

Jacques Schneider (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Approximation theory in the context of probability density function turns out to go beyond the classical idea of orthogonal projection. Special tools have to be designed so as to respect the nonnegativity of the approximate function. We develop here and justify from the theoretical point of view an approximation procedure introduced by Levermore [Levermore, J. Stat. Phys. 83 (1996) 1021–1065] and based on an entropy minimization principle under moment constraints. We prove in particular a global...

Entropic approximation in kinetic theory

Jacques Schneider (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Approximation theory in the context of probability density function turns out to go beyond the classical idea of orthogonal projection. Special tools have to be designed so as to respect the nonnegativity of the approximate function. We develop here and justify from the theoretical point of view an approximation procedure introduced by Levermore [Levermore, J. Stat. Phys.83 (1996) 1021–1065] and based on an entropy minimization principle under moment constraints. We prove in particular...

Entropic Projections and Dominating Points

Christian Léonard (2010)

ESAIM: Probability and Statistics

Entropic projections and dominating points are solutions to convex minimization problems related to conditional laws of large numbers. They appear in many areas of applied mathematics such as statistical physics, information theory, mathematical statistics, ill-posed inverse problems or large deviation theory. By means of convex conjugate duality and functional analysis, criteria are derived for the existence of entropic projections, generalized entropic projections and dominating points. Representations...

Entropy and approximation numbers of embeddings between weighted Besov spaces

Iwona Piotrowska (2008)

Banach Center Publications

The present paper is devoted to the study of the “quality” of the compactness of the trace operator. More precisely, we characterize the asymptotic behaviour of entropy numbers of the compact map t r Γ : B p ₁ , q s ( ℝ ⁿ , w ϰ Γ ) → L p ₂ ( Γ ) , where Γ is a d-set with 0 < d < n and w ϰ Γ a weight of type w ϰ Γ ( x ) d i s t ( x , Γ ) ϰ near Γ with ϰ > -(n-d). There are parallel results for approximation numbers.

Entropy numbers of embeddings of Sobolev spaces in Zygmund spaces

D. Edmunds, Yu. Netrusov (1998)

Studia Mathematica

Let id be the natural embedding of the Sobolev space W p l ( Ω ) in the Zygmund space L q ( l o g L ) a ( Ω ) , where Ω = ( 0 , 1 ) n , 1 < p < ∞, l ∈ ℕ, 1/p = 1/q + l/n and a < 0, a ≠ -l/n. We consider the entropy numbers e k ( i d ) of this embedding and show that e k ( i d ) ≍ k - η , where η = min(-a,l/n). Extensions to more general spaces are given. The results are applied to give information about the behaviour of the eigenvalues of certain operators of elliptic type.

Entropy numbers of general diagonal operators.

Thomas Kühn (2005)

Revista Matemática Complutense

We determine the asymptotic behavior of the entropy numbers of diagonal operators D: lp → lq, (xk) → (skxk), 0 &lt; p,q ≤ ∞, under mild regularity and decay conditions on the generating sequence (σk). Our results extend the known estimates for polynomial and logarithmic diagonals (σk). Moreover, we also consider some exotic intermediate examples like (σk)=exp(-√log k).

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