Littlewood-Paley-Stein functionals

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Littlewood-Paley-Stein functionals: an R-boundedness approach

Littlewood-Paley-Stein functionals: an R-boundedness approach

We apply Theorems 4.1 and 4.2 to obtain general Littlewood-Paley-Stein estimates on L p (R n ) for p in one of intervals given in Theorem 7.2. Their reverse inequalities proved in Section 6 hold on the dual space. It is also proved in [34] that the above range is optimal for the boundedness of the Riesz transform. One may then ask whether this range is optimal for the boundedness of the Littlewood-Paley-Stein functional as well. This is indeed the case.

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Conical square functionals on Riemannian manifolds

Conical square functionals on Riemannian manifolds

[13] Thierry Coulhon, Xuan Thinh Duong, and Xiang Dong Li. LittlewoodPaleyStein functions on complete Riemannian manifolds for 1 ≤ p ≤ 2. Studia Mathematica, 154(1):3757, 2003. [14] Michael Cowling, Ian Doust, Alan McIntosh, and Atsushi Yagi. Banach space oper- ators with a bounded H ∞ functional calculus. J. Austral. Math. Soc. Ser. A, pages

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Littlewood-Paley functionals on graphs

Littlewood-Paley functionals on graphs

[15] N. Dungey. A Littlewood-Paley-Stein estimate on graphs and groups. Studia Mathematica, 189(2):113–129, 2008. [16] C. Fefferman and E. M. Stein. Some maximal inequalities. Amer. J. Math., 93:107–115, 1971. [17] P. Hajlasz and P. Koskela. Sobolev met Poincaré. Mem. Amer. Math. Soc., 145(688), 2000. [18] E. Russ. Riesz tranforms on graphs for 1 ≤ p ≤ 2. Math. Scand., 87(1):133–160, 2000. [19] E. M. Stein. On the Maximal Ergodic Theorem. Proc. Nat. Acad. Sci., 47:1894–1897, 1961. [20] E. M. Stein. Singular integrals and differentiability properties of functions. Princeton Mathematical
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Some unexpected properties of Littlewood-Richardson coefficients

Some unexpected properties of Littlewood-Richardson coefficients

λµ : ν ∈ Λ n } and {c ν λ ∗ µ : ν ∈ Λ n } are expected to be equal, if λ is near-rectangular. In the literature, there are a lot of equalities between Littlewood-Richardson coefficients. There are symmetries (see [BR20] and references therein), stabilities (see [BOR15]), re- ductions (see [CM11]). None of this numerous results seems to explain that Conjecture 1 holds even for GL 3 (C). Moreover, there are various combinatorial models for the Littlewood-

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Théorème de Paley-Wiener suivant le dual unitaire d'un groupe compact

Théorème de Paley-Wiener suivant le dual unitaire d'un groupe compact

Abstract Paley Wiener theorem characterizes the class of functions which are Fourier transforms of C ∞ functions of compact support on R n by relating decay properties of those functions or distributions at infinity with analyticity of their Fourier transform. The theorem is already proved in classical case : the real case with holomorphic Fourier transform on L 2 (R), the case of functions with compact support on R n from Hörmander and the spherical transform on semi simple Lie groups with Gangolli theorem.

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On a mixed Littlewood conjecture for quadratic numbers

On a mixed Littlewood conjecture for quadratic numbers

R´ esum´ e. Nous ´ etudions un probl` eme diophantien simultan´ e reli´ e ` a la conjecture de Littlewood. En utilisant des minorations con- nues de formes lin´ eaires de logarithmes p-adiques, nous montrons qu’un r´ esultat que nous avons pr´ ec´ edemment obtenu, concernant les nombres quadratiques, est presque optimal.

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Subdifferentiation of integral functionals

Subdifferentiation of integral functionals

9 Legendre functions and integral functionals A kind of duality for nonconvex functions has been designed by Ekeland [13], [12] and adapted by the second author to the use of subdi¤erentials [40], [39], [38]. It encompasses the Fenchel conjugacy. Since the preceding gives some knowledge of the subdi¤erentials of integral functionals, it is natural to examine its application to such a class of functionals. The case of functionals on L p (S; E) with p > 1 di¤ers from the case of integral

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Théorème de Paley-Wiener pour les fonctions de Whittaker sur un groupe réductif p-adique

Théorème de Paley-Wiener pour les fonctions de Whittaker sur un groupe réductif p-adique

c (U 0 \G, ψ) l’espace des ´el´ements de C ∞ (U 0 \G, ψ) qui sont `a support compact modulo U 0 . Le but de cet article est de d´efinir une transform´ee de Fourier pour cet espace et d’en caract´eriser l’image. Ce Th´eor`eme est l’analogue pour les fonctions de Whittaker du Th´eor`eme de Paley-Wiener pour les fonctions sur le groupe, du `a Joseph Bernstein [B2] et dont Heiermann [H] a fourni une autre preuve. Ici, c’est le travail d’Heiermann qui sert de fil conducteur `a notre preuve.

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Stein operators for product distributions, with applications

Stein operators for product distributions, with applications

The first key to setting up Stein’s method for a target X is of course to identify the operator A X . A general canonical theory is available in [25], upon which we shall dwell in Section 1.3. Many general theories have been proposed in recent years. These are relatively easy to setup under specific assumptions on the target density, see https://sites.google.com/site/steinsmethod/ for an overview of the quite large literature on this topic. In the case where the target has a density with respect to the Lebesgue measure, an assumption which we impose from here onwards, then adhoc duality arguments are easy to apply for targets X whose densities satisfy explicit differential equations. For instance the p.d.f. γ(x) = (2π) −1/2 e −x 2 /2 of the standard normal distribution satisfies the first order ODE γ 0 (x) + xγ(x) = 0 leading, by integration by parts, to the well-known operator Af (x) = f 0 (x) − xf (x). By a similar reasoning, natural first order operators are easy to devise for target distributions which belong to the Pearson family [37] or which satisfy a diffusive assumption [8, 23]. There is a priori no reason for which the characterizing operator should be of first order and a very classical example is the above mentioned standard normal operator which is often viewed as Af (x) = f 00 (x) − xf 0 (x), the generator of an Ornstein-Uhlenbeck process (see, for example, [3]). Higher order operators whose order can not be trivially reduced are also available : [14] obtains a second order operator for the entire family of variance-gamma distributions (see also [16]), [35] obtain a second order Stein operator for the Laplace distribution, and [33] obtain a second order operator for the PRR distribution, which has a density that can be expressed in terms of the Kummer U function. More generally, if the p.d.f. of X is defined in terms of special functions (Kummer U , Meijer G, Bessel, etc.) which are themselves defined as solutions to explicit dth order differential equations then the duality approach shall yield a tractable differential operator with explicit coefficients.
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Sur les espaces de Stein quasi-compacts en géométrie rigide

Sur les espaces de Stein quasi-compacts en géométrie rigide

DÉFINITION 3. On dit qu’un espace analytique rigide quasi-compact séparé X est un S-espace s’il est holomorphiquement séparable (i.e. pour tout x -7É y dans X, il existe f E Ox (X) tel que f(x) = 0 et f(y) = 1) et si = 0 pour tout q > 1. Ainsi tout espace de Stein quasi-compact est un S-espace.

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Stein Block Thresholding For Image Denoising

Stein Block Thresholding For Image Denoising

4 Conclusion In this paper, a Stein block thresholding algorithm for denoising d-dimensional data is proposed with a particular focus on 2D image. Our block denoising is a generalization of one-dimensional BlockJS to d dimensions, with other trans- forms than orthogonal wavelets, and handles noise in the coefficient domain beyond the i.i.d. Gaussian case. Its minimax properties are investigated, and a fast and appealing algorithm is described. The practical performance of the designed denoiser were shown to be very promising with several transforms and a variety of test images. It turns out that the proposed block denoiser is much faster than state-of-the art competitors in the literature while reaching comparable denoising performance.
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Image Deconvolution by Stein Block Thresholding

Image Deconvolution by Stein Block Thresholding

There is an extensive statistical literature on wavelet- based deconvolution problems. For obvious space limita- tions, we only focus on some of them. In 1D, Donoho in [1] gave the first discussion of wavelet thresholding in lin- ear inverse problems and introduced the Wavelet-Vaguelet Decomposition (WVD). The WaveD algorithm of [2] is an adaptation of WVD to the one dimensional deconvolution problem. Abramovich and Silverman in [3] proposed another procedure; the Vaguelet-Wavelet Decomposition (VWD). The original estimator based on VWD is defined with stan- dard term-by-term thresholding rules. It has been improved by [4] using a Stein block thresholding rule. As for VWD, the original WaveD procedure based on term-by-term thresh- olding has been recently improved by [5] using again block thresholding.
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Asymptotic analysis of shape functionals

Asymptotic analysis of shape functionals

Unit´e de recherche INRIA Rocquencourt Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex France Unit´e de recherche INRIA Lorraine : LORIA, Technopˆole de Nancy-Braboi[r]

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Un théorème de Paley-Wiener matriciel pour un groupe réductif p-adique non connexe

Un théorème de Paley-Wiener matriciel pour un groupe réductif p-adique non connexe

[10] David Renard. Repr´esentations des groupes r´eductifs p-adiques. Ecole Polytechnique, 2008. Manuscrit. [11] J. D. Rogawski. Trace Paley-Wiener theorem in the twisted case. Trans. Amer. Math. Soc., 309(1) :215– 229, 1988. [12] Allan J. Silberger. Introduction to harmonic analysis on reductive p-adic groups, volume 23 of Mathe- matical Notes. Princeton University Press, Princeton, N.J., 1979. Based on lectures by Harish-Chandra at the Institute for Advanced Study, 1971–1973.

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A note on time-dependent additive functionals

A note on time-dependent additive functionals

A note on time-dependent additive functionals Adrien BARRASSO ∗ Francesco RUSSO † August 2nd 2017 Abstract. This note develops shortly the theory of time-inhomogeneous additive functionals and is a useful support for the analysis of time-dependent Markov processes and related topics. It is a significant tool for the analysis of BSDEs in law. In particular we extend to a non-homogeneous setup some results concerning the quadratic variation and the angular bracket of Martin- gale Additive Functionals (in short MAF) associated to a homogeneous Markov processes.

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Stein block thresholding for wavelet-based image deconvolution

Stein block thresholding for wavelet-based image deconvolution

There is an extensive statistical literature on wavelet-based deconvolution problems. For obvious space limitations, we only focus on some of them. In 1D, Donoho in [ 10 ] gave the first discussion of wavelet thresholding in linear inverse problems and introduced the Wavelet-Vaguelet Decomposition (WVD). The WaveD algorithm as described in [ 13 ] is an adaptation of WVD to the one-dimensional deconvolution problem. Abramovich and Silverman in [ 1 ] pro- posed another procedure; the Vaguelet-Wavelet Decomposition (VWD). The VWD estimator in its original form relies on standard term-by-term threshold- ing rules. It has been improved by Cai in [ 3 ] using a Stein block thresholding rule. In the same vein as the block extension of VWD, the original term-by-term thresholding-based WaveD procedure has been recently enhanced by Chesneau [ 5 ] using again block thresholding.
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Type de narrateur et place du lecteur dans "Le Ravissement de Lol V. Stein"

Type de narrateur et place du lecteur dans "Le Ravissement de Lol V. Stein"

vérité comme pure croyance, et la voix de l'auteur, comme simple hypothèse et non comme thèse. Le passage au récit homodiégétique affirme la thèse épistémique de Duras : il met en œuvre le "vrai" type de connaissance, le savoir affectif non théorisé, celui de la relation vécue par le personnage-narrateur avec Lol. Le narrateur dit : "Je connais Lol V. Stein de la seule façon que je puisse, d'amour. C'est en raison de cette connaissance que je suis arrivé à croire ceci:". L'objectif de l'écriture durassienne est de faire partager au lecteur l'expérience affective des personnages hors verbalisation conceptuelle, ou récit psychologisant 9 .
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L'Einfühlung chez Husserl et Edith Stein : la constitution intersubjective du sujet

L'Einfühlung chez Husserl et Edith Stein : la constitution intersubjective du sujet

m’éloigner des autres choses. En me tournant, elles sont tantôt à ma gauche puis à ma droite. ii) Il est limité dans la diversité de ses apparences Tandis que les choses du monde peuvent varier dans leur apparence de façon infinie selon la possibilité du sujet de se mouvoir librement et de changer sa position par rapport à elles, les différentes apparences du corps propre sont cependant limitées : « je ne peux voir certaines parties du corps que dans un raccourci perspectif tout à fait particulier, et d’autres sont pour moi franchement impossibles à voir (par exemple ma tête). Ce même corps, qui me sert de moyen pour toutes les perceptions, me fait obstacle dans la perception de lui-même et il est une chose dont la constitution est étonnamment imparfaite 100 . » Similairement, Stein note comment l’apparaître du corps s’accompagne de curieuses lacunes : « qui me refuse la vue de sa face arrière avec plus d’obstination encore que la lune, qui se joue de moi en m’incitant à le considérer sous des faces toujours nouvelles et me les dissimulant dès que je veux obéir à son invitation 101 . » À l’inverse, les autres choses du monde sont saisissables, retournables, il est
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Littlewood reliability model for modular software and Poisson approximation

Littlewood reliability model for modular software and Poisson approximation

restarted instantaneously. An important issue in reliability theory, specifically for software systems, is what happens when the failure parameters tend to be smaller and smaller. Littlewood stated in (Littlewood 1975) As all failure parameters µ(i),µ(i, j) tend to zero, the failure process described above is asymptotically a HPP with intensity

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Dimensional reduction for supremal functionals

Dimensional reduction for supremal functionals

These kind of problems have been widely studied in the framework of integral functionals by means of Γ-convergence analysis. Indeed Γ-convergence, which has been introduced in [31] (see also [28, 17, 18] for detailed discussions on that subject), turns out to be well adapted for studying the asymptotic behavior of variational problems depending on a parameter because it gives good informations on the asymptotics of minimizers and of the minimal value.

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