Présentation jordanienne de l'algèbre de Weyl A₂

J. Alev; F. Dumas

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Idéaux fermés de certaines algèbres de Beurling et application aux opérateurs à spectre dénombrable

Cyril Agrafeuil (2005)

Studia Mathematica

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We denote by the unit circle and by the unit disc of ℂ. Let s be a non-negative real and ω a weight such that $ω (n) = {(1 + n)}^{s}$ (n ≥ 0) and the sequence ${(ω (- n) / {(1 + n)}^{s})}_{n \geq 0}$ is non-decreasing. We define the Banach algebra $A_{ω} () = {f \in () : | | f | |}_{ω} = \sum_{n = - \infty}^{+ \infty} | f ̂ (n) | ω (n) < + \infty$ . If I is a closed ideal of $A_{ω} ()$ , we set $h ⁰ (I) = z \in : f (z) = 0 (f \in I)$ . We describe all closed ideals I of $A_{ω} ()$ such that h⁰(I) is at most countable. A similar result is obtained for closed ideals of the algebra $A ⁺_{s} () = f \in A_{ω} () : f ̂ (n) = 0 (n < 0)$ without inner factor. Then we use this description to establish a link between operators with countable spectrum and interpolating...

Sur les courbes hyperelliptiques cyclotomiques et les équations $x^{p} - y^{p} = c z ²$

Wilfrid Ivorra

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Let p be a prime number ≥ 11 and c be a square-free integer ≥ 3. In this paper, we study the diophantine equation $x^{p} - y^{p} = c z ²$ in the case where p belongs to 11,13,17. More precisely, we prove that for those primes, there is no integer solution (x,y,z) to this equation satisfying gcd(x,y,z) = 1 and xyz ≠ 0 if the integer c has the following property: if ℓ is a prime number dividing c then ℓ ≢ 1 mod p. To obtain this result, we consider the hyperelliptic curves $C_{p} : y ² = Φ_{p} (x)$ and $D_{p} : p y ² = Φ_{p} (x)$ , where $Φ_{p}$ is the pth cyclotomic...

Sur un problème de Rényi et Ivić concernant les fonctions de diviseurs de Piltz

Rimer Zurita (2013)

Acta Arithmetica

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Let Ω(n) and ω(n) denote the number of distinct prime factors of the positive integer n, counted respectively with and without multiplicity. Let $d_{k} (n)$ denote the Piltz function (which counts the number of ways of writing n as a product of k factors). We obtain a precise estimate of the sum $\sum_{n \leq x, Ω (n) - ω (n) = q} f (n)$ for a class of multiplicative functions f, including in particular $f (n) = d_{k} (n)$ , unconditionally if 1 ≤ k ≤ 3, and under some reasonable assumptions if k ≥ 4. The result also applies to f(n) = φ(n)/n (where φ is...

Fonctions maximales centrées de Hardy-Littlewood sur les groupes de Heisenberg

Hong-Quan Li (2009)

Studia Mathematica

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By getting uniformly asymptotic estimates for the Poisson kernel on Heisenberg groups $ℍ_{2 n + 1}$ , we prove that there exists a constant A > 0, independent of n ∈ ℕ*, such that for all $f \in L ¹ (ℍ_{2 n + 1})$ , we have ${| | M f | |}_{L^{1, \infty}} \leq A n | | f | | ₁$ , where M denotes the centered Hardy-Littlewood maximal function defined by the Carnot-Carathéodory distance or by the Korányi norm.

Inégalités à poids pour l'opérateur de Hardy-Littlewood-Sobolev dans les espaces métriques mesurés à deux demi-dimensions

David Mascré (2006)

Colloquium Mathematicae

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On a metric measure space (X,ϱ,μ), consider the weight functions $w_{α} (x) = ϱ {(x, z ₀)}^{- α ₀}$ if ϱ(x,z₀) < 1, $w_{α} (x) = ϱ {(x, z ₀)}^{- α ₁}$ if ϱ(x,z₀) ≥ 1, $w_{β} (x) = ϱ {(x, z ₀)}^{- β ₀}$ if ϱ(x,z₀) < 1, $w_{β} (x) = ϱ {(x, z ₀)}^{- β ₁}$ if ϱ(x,z₀) ≥ 1, where z₀ is a given point of X, and let $κ_{a} : X \times X \to ℝ ₊$ be an operator kernel satisfying $κ_{a} (x, y) \leq c ϱ {(x, y)}^{a - d}$ for all x,y ∈ X such that ϱ(x,y) < 1, $κ_{a} (x, y) \leq c ϱ {(x, y)}^{a - D}$ for all x,y ∈ X such that ϱ(x,y)≥ 1, where 0 < a < min(d,D), and d and D are respectively the local and global volume growth rate of the space X. We determine conditions on a, α₀, α₁, β₀, β₁ ∈ ℝ for the Hardy-Littlewood-Sobolev...

Une formule pour les extensions de foncteurs composés

Alain Troesch (2003)

Fundamenta Mathematicae

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Let p be a prime, and let ℱ be the category of functors from the finite $_{p}$ -vector spaces to all $_{p}$ -vector spaces. The object Id of ℱ is the inclusion functor. Let F and G be two objects in ℱ. If F and G satisfy suitable conditions, the main result of this paper allows one to compute $E x t *_{ℱ} (I d, G \circ F)$ from the knowledge of $E x t *_{ℱ} (I d, F)$ and $E x t *_{ℱ} (I d, G)$ .

Espaces BMO, inégalités de Paley et multiplicateurs idempotents

Hubert Lelièvre (1997)

Studia Mathematica

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Generalizing the classical BMO spaces defined on the unit circle with vector or scalar values, we define the spaces $B M O_{ψ_{q}} ()$ and $B M O_{ψ_{q}} (, B)$ , where $ψ_{q} (x) = e^{x^{q}} - 1$ for x ≥ 0 and q ∈ [1,∞[, and where B is a Banach space. Note that $B M O_{ψ_{1}} () = B M O ()$ and $B M O_{ψ_{1}} (, B) = B M O (, B)$ by the John-Nirenberg theorem. Firstly, we study a generalization of the classical Paley inequality and improve the Blasco-Pełczyński theorem in the vector case. Secondly, we compute the idempotent multipliers of $B M O_{ψ_{q}} ()$ . Pisier conjectured that the supports of idempotent multipliers of...

Feuilletages holomorphes de codimension un dont la classe canonique est triviale

Frédéric Touzet (2008)

Annales scientifiques de l'École Normale Supérieure

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We give a description of Kähler manifolds $M$ equipped with an integrable subbundle $ℱ$ of $T M$ of rank $n - 1$ ( $n = \dim M$ ) under the assumption that the line bundle $D é t ℱ$ is numerically trivial. This is a sort of foliated version of Bogomolov’s theorem concerning Kähler manifolds with trivial canonical class.

$L^{p} (G, X )$ comme sous-espace complémenté de $L^{q} (G, X) $

Mohammad Daher (2013)

Colloquium Mathematicae

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Let G be a compact metric infinite abelian group and let X be a Banach space. We study the following question: if the dual X* of X does not have the Radon-Nikodym property, is $L^{p} (G, X *)$ complemented in $L^{q} (G, X) *$ , 1 < p ≤ ∞, 1/p + 1/q = 1, or, if p = 1, in the subspace of C(G,X)* consisting of the measures that are absolutely continuous with respect to the Haar measure? We show that the answer is negative if X is separable and does not contain ℓ¹, and if 1 ≤ p < ∞. If p = 1, this answers a question...

Les -types du système $ℱ$

K. Nour (2010)

RAIRO - Theoretical Informatics and Applications

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We prove in this paper that the types of system $ℱ$ inhabited uniquely by λ-terms (the -types) have a positive quantifier. We give also consequences of this result and some examples.

Générateurs de l’algèbre $𝒰 {(G)}^{K}$ avec $G = S O (m)$ ou $S O_{o} (1, m - 1)$ et $K = S O (m - 1)$

Abdel-Ilah Benabdallah (1982)

Publications du Département de mathématiques (Lyon)

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Groupe des classes projectives d’un ordre $𝒟$ de $ℤ$ dans l’algèbre du groupe diédral d’ordre $2 p$ sur $𝐐$

Anne-Marie Bergé (1969-1970)

Séminaire de théorie des nombres de Bordeaux

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Sur un problème parabolique-elliptique

Philippe Benilan, Petra Wittbold (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We prove existence (uniqueness is easy) of a weak solution to a boundary value problem for an equation like ${(v - 1)}_{t}^{+} = v_{x x} + F {(v)}_{x}$ where the function $F : ℝ \to ℝ$ is only supposed to be locally lipschitz continuous. In order to replace the lack of compactness in on , we use nonlinear semigroup theory.

Derivees tangentielles des fonctions de la classe $^{k, α}$ dans les domaines de type fini de ℂ²

Laurent Verdoucq (2002)

Annales Polonici Mathematici

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Let Ω be a domain of finite type in ℂ² and let f be a function holomorphic in Ω and belonging to $^{k, α} (Ω ̅)$ . We prove the existence of boundary values for some suitable derivatives of f of order greater than k. The gain of derivatives holds in the complex-tangential direction and it is precisely related to the geometry of ∂Ω. Then we prove a property of non-isotropic Hölder regularity for these boundary values. This generalizes some results given by J. Bruna and J. M. Ortega for the unit ball. ...

Stabilité $L^{1}$ d’ondes progressives de lois de conservation scalaires

Denis Serre (1998-1999)

Séminaire Équations aux dérivées partielles

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A powerfull method has been developped in [2] for the study of $L^{1}$ -stability of travelling waves in conservation laws or more generally in equations which display $L^{1}$ -contractivity, maximum principle and mass conservation. We recall shortly the general procedure. We also show that it partly applies to the waves of a model of radiating gas. These waves have first been studied by Kawashima and Nishibata [5,6] in a different framework. Therefore, shock fronts for this model are stable under...

Démonstration de l’irrationalité de $ζ (3)$ (d’après R. Apery)

Henri Cohen (1977-1978)

Séminaire de théorie des nombres de Grenoble

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Platitude du module universel pour ${GL}_{3}$ en caractéristique non banale

Joël Bellaïche, Ania Otwinowska (2003)

Bulletin de la Société Mathématique de France

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Soient $F$ un corps $p$ -adique, $G = {GL}_{3} (F)$ . Pour $χ$ un caractère de l’algèbre de Hecke sphérique de $G$ sur un anneau commutatif $k$ , on introduit à la suite de Serre une représentation lisse $M_{χ}$ de $G$ sur $k$ qui gouverne la théorie des représentations non ramifiées de $G$ sur $k$ . Nous prouvons que $M_{χ}$ est plat sur $k$ et que si $p$ est inversible dans $k$ , alors pour tout sous-groupe compact ouvert suffisament petit $U$ de $G$ , le module $M_{χ}^{U}$ est libre de rang fini sur $k$ . Ceci était conjecturé par Lazarus. Comme corollaire,...

Propriétés q-multiplicatives de la suite $⌊ n^{c} ⌋$ , c > 1

Christian Mauduit, Joël Rivat (2005)

Acta Arithmetica

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Propriétés (Q) et (C). Variété commutante

Jean-Yves Charbonnel (2004)

Bulletin de la Société Mathématique de France

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Soient $X$ une variété algébrique complexe, lisse, irréductible, $E$ et $F$ deux espaces vectoriels complexes de dimension finie et $μ$ un morphisme de $X$ dans l’espace Lin $(E, F)$ des applications linéaires de $E$ dans $F$ . Pour $x \in X$ , on note $E (x)$ et $x \cdot E$ le noyau et l’image de $μ (x)$ , ${\bar{μ}}_{x}$ le morphisme de $X$ dans Lin $(E (x), F / (x \cdot E))$ qui associe à $y$ l’application linéaire $v \mapsto μ (y) (v) + x \cdot E$ . Soit i $_{μ}$ la dimension minimale de $E (x)$ . On dit que $μ$ asi i $_{{\bar{μ}}_{x}}$ est inférieur à i $_{μ}$ . Soient $F^{*}$ le dual de $F$ , S $(F)$ l’algèbre symétrique de $F$ , $ℐ_{μ}$ l’idéal de $𝒪_{X} \otimes_{ℂ} S (F)$ engendré par les fonctions...