## Displaying similar documents to “${L}^{p}\left(G,X*\right)$ comme sous-espace complémenté de ${L}^{q}\left(G,X\right)*$”

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

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 $\omega \left(n\right)={\left(1+n\right)}^{s}$ (n ≥ 0) and the sequence ${\left(\omega \left(-n\right)/{\left(1+n\right)}^{s}\right)}_{n\ge 0}$ is non-decreasing. We define the Banach algebra ${A}_{\omega }\left(\right)={f\in \left(\right):||f||}_{\omega }={\sum }_{n=-\infty }^{+\infty }|f̂\left(n\right)|\omega \left(n\right)<+\infty$. If I is a closed ideal of ${A}_{\omega }\left(\right)$, we set $h⁰\left(I\right)=z\in :f\left(z\right)=0\left(f\in I\right)$. We describe all closed ideals I of ${A}_{\omega }\left(\right)$ such that h⁰(I) is at most countable. A similar result is obtained for closed ideals of the algebra $A{⁺}_{s}\left(\right)=f\in {A}_{\omega }\left(\right):f̂\left(n\right)=0\left(n<0\right)$ without inner factor. Then we use this description to establish a link between operators with countable spectrum and interpolating...

### Ground states of supersymmetric matrix models

Séminaire Équations aux dérivées partielles

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We consider supersymmetric matrix Hamiltonians. The existence of a zero-energy bound state, in particular for the $d=9$ model, is of interest in M-theory. While we do not quite prove its existence, we show that the decay at infinity such a state would have is compatible with normalizability (and hence existence) in $d=9$. Moreover, it would be unique. Other values of $d$, where the situation is somewhat different, shall also be addressed. The analysis is based on a Born-Oppenheimer approximation....

### Théorèmes de préparation Gevrey et étude de certaines applications formelles

Annales Polonici Mathematici

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We consider subrings A of the ring of formal power series. They are defined by growth conditions on coefficients such as, for instance, Gevrey conditions. We prove preparation theorems of Malgrange type in these rings. As a consequence we study maps F from ${ℂ}^{s}$ to ${ℂ}^{p}$ without constant term such that the rank of the Jacobian matrix of F is equal to 1. Let be a formal power series. If F is a holomorphic map, the following result is well known: ∘ F is analytic implies there exists a convergent...

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

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 ${}^{k,\alpha }\left(\Omega ̅\right)$. 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. ...

### Espaces de suites réelles complètement métrisables

Fundamenta Mathematicae

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Let X be an hereditary subspace of the Polish space ${ℝ}^{\omega }$ of real sequences, i.e. a subspace such that [x = (xₙ)ₙ ∈ X and ∀n, |yₙ| ≤ |xₙ|] ⇒ y = (yₙ)ₙ ∈ X. Does X admit a complete metric compatible with its vector structure? We have two results: ∙ If such an X has a complete metric δ, there exists a unique pair (E,F) of hereditary subspaces with E ⊆ X ⊆ F, (E,δ) complete separable, and F complete maximal in a strong sense. On E and F, the metrics have a simple form, and the spaces E are...

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

Studia Mathematica

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By getting uniformly asymptotic estimates for the Poisson kernel on Heisenberg groups ${ℍ}_{2n+1}$, we prove that there exists a constant A > 0, independent of n ∈ ℕ*, such that for all $f\in L¹\left({ℍ}_{2n+1}\right)$, we have ${||Mf||}_{{L}^{1,\infty }}\le An||f||₁$, where M denotes the centered Hardy-Littlewood maximal function defined by the Carnot-Carathéodory distance or by the Korányi norm.

### Présentation jordanienne de l'algèbre de Weyl A₂

Annales Polonici Mathematici

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Let k be a commutative field. For any a,b∈ k, we denote by ${J}_{a,b}\left(k\right)$ the deformation of the 2-dimensional Weyl algebra over k associated with the Jordanian Hecke symmetry with parameters a and b. We prove that: (i) any ${J}_{a,b}\left(k\right)$ can be embedded in the usual Weyl algebra A₂(k), and (ii) ${J}_{a,b}\left(k\right)$ is isomorphic to A₂(k) if and only if a = b.

### Sur la classification des séries discrètes des groupes classiques p-adiques: paramètres de Langlands et exhaustivité

Journal of the European Mathematical Society

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In this paper, we are giving parameters for discrete series of classical $p$-adic groups. We first define: the analogous of the Langlands morphism of ${W}_{F}$ in the $L$-group, part of the analogous of the character of the centralizer of that morphism and, to supply the missing part of the full definition of that character, the cuspidal support of the representation. Then, we state an hypothesis on the reducibility points for induced of cuspidal representations. And we prove that, under this hypothesis,...

### Sur les courbes hyperelliptiques cyclotomiques et les équations ${x}^{p}-{y}^{p}=cz²$

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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 ${x}^{p}-{y}^{p}=cz²$ 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 ${C}_{p}:y²={\Phi }_{p}\left(x\right)$ and ${D}_{p}:py²={\Phi }_{p}\left(x\right)$, where ${\Phi }_{p}$ is the pth cyclotomic...

### Les types de données syntaxiques du système $ℱ$

RAIRO - Theoretical Informatics and Applications

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We give in this paper a purely syntactical definition of input and output types of system $ℱ$. We define the syntactical data types as input and output types. We show that any type with positive quantifiers is a syntactical data type and that an input type is an output type. We give some restrictions on the -elimination rule in order to prove that an output type is an input type.

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

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 ${d}_{k}\left(n\right)$ 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 ${\sum }_{n\le x,\Omega \left(n\right)-\omega \left(n\right)=q}f\left(n\right)$ for a class of multiplicative functions f, including in particular $f\left(n\right)={d}_{k}\left(n\right)$, 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...

### Sur un problème parabolique-elliptique

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 ${\left(v-1\right)}_{t}^{+}={v}_{xx}+F{\left(v\right)}_{x}$ 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.

### Les -types du système $ℱ$

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.

### Plus grand facteur premier de valeurs de polynômes aux entiers

Acta Arithmetica

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Let P⁺(n) denote the largest prime factor of the integer n. Using the Heath-Brown and Dartyge methods, we prove that for any even unitary irreducible quartic polynomial Φ with integral coefficients and the associated Galois group isomorphic to V₄, there exists a positive constant ${c}_{\Phi }$ such that the set of integers n ≤ X satisfying $P⁺\left(\Phi \left(n\right)\right)\ge {X}^{1+{c}_{\Phi }}$ has a positive density. Such a result was recently proved by Dartyge for Φ(n) = n⁴ - n² + 1. There is an appendix written with Jean-François Mestre. ...

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

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...

### Une formule pour les extensions de foncteurs composés

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 $Ext{*}_{ℱ}\left(Id,G\circ F\right)$ from the knowledge of $Ext{*}_{ℱ}\left(Id,F\right)$ and $Ext{*}_{ℱ}\left(Id,G\right)$.

### Espaces BMO, inégalités de Paley et multiplicateurs idempotents

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 $BM{O}_{{\psi }_{q}}\left(\right)$ and $BM{O}_{{\psi }_{q}}\left(,B\right)$, where ${\psi }_{q}\left(x\right)={e}^{{x}^{q}}-1$ for x ≥ 0 and q ∈ [1,∞[, and where B is a Banach space. Note that $BM{O}_{{\psi }_{1}}\left(\right)=BMO\left(\right)$ and $BM{O}_{{\psi }_{1}}\left(,B\right)=BMO\left(,B\right)$ 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 $BM{O}_{{\psi }_{q}}\left(\right)$. Pisier conjectured that the supports of idempotent multipliers of...

### Courbes elliptiques sur ℚ, ayant un point d’ordre 2 rationnel sur ℚ, de conducteur ${2}^{N}p$

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Let p be a prime number ≥ 29 and N be a positive integer. In this paper, we are interested in the problem of the determination, up to ℚ-isomorphism, of all the elliptic curves over ℚ whose conductor is ${2}^{N}p$, with at least one rational point of order 2 over ℚ. This problem was studied in 1974 by B. Setzer in case N = 0. Consequently, in this work we are concerned with the case N ≥ 1. The results presented here are analogous to those obtained by B. Setzer and allow one in practice to find...

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

Colloquium Mathematicae

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On a metric measure space (X,ϱ,μ), consider the weight functions ${w}_{\alpha }\left(x\right)=\varrho {\left(x,z₀\right)}^{-\alpha ₀}$ if ϱ(x,z₀) < 1, ${w}_{\alpha }\left(x\right)=\varrho {\left(x,z₀\right)}^{-\alpha ₁}$ if ϱ(x,z₀) ≥ 1, ${w}_{\beta }\left(x\right)=\varrho {\left(x,z₀\right)}^{-\beta ₀}$ if ϱ(x,z₀) < 1, ${w}_{\beta }\left(x\right)=\varrho {\left(x,z₀\right)}^{-\beta ₁}$ if ϱ(x,z₀) ≥ 1, where z₀ is a given point of X, and let ${\kappa }_{a}:X×X\to ℝ₊$ be an operator kernel satisfying ${\kappa }_{a}\left(x,y\right)\le c\varrho {\left(x,y\right)}^{a-d}$ for all x,y ∈ X such that ϱ(x,y) < 1, ${\kappa }_{a}\left(x,y\right)\le c\varrho {\left(x,y\right)}^{a-D}$ 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...

### Feuilletage canonique sur le fibré de Weil

Colloquium Mathematicae

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Let be M a smooth manifold, A a local algebra and ${M}^{A}$ a manifold of infinitely near points on M of kind A. We build the canonical foliation on ${M}^{A}$ and we show that the canonical foliation on the tangent bundle TM is the foliation defined by its canonical field.

### Pinceaux de courbes planes et invariants polaires

Annales Polonici Mathematici

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We study pencils of plane curves ${f}_{t}=f-t{l}^{N}$, t ∈ ℂ, using the notion of polar invariant of the plane curve f = 0 with respect to a smooth curve l = 0. More precisely we compute the jacobian Newton polygon of the generic fiber ${f}_{t}$, t ∈ ℂ. The main result gives the description of pencils which have an irreducible fiber. Furthermore we prove some applications of the local properties of pencils to singularities at infinity of polynomials in two complex variables.