Remarques sur un mémoire d'Hermite

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Remarques sur un algorithme d'optimisation pour une classe de fonctionnelles sur ℝk

We give a quite elementary proof of the convergence of an optimization algorithm for nonconvex functional on ℝ^k which are experimentally efficient in numerical Imaging.     

Interpolation polyn?miale sur un ordre d’un corps de nombres

Résumé  Dans ce texte, nous introduisons des polyn?mes d’interpolation sur un ordre d’un corps de nombres qui généralisent les polyn?mes bin?miaux usuels. Comme application, on montre, en utilisant ces polyn?mes, qu’une fonction entière envoyant un ordre d’un corps de nombres dans l’anneau des entiers de ce corps et dont les croissances analytique et arithmétique sont faibles est un polyn?me, étendant ainsi au cas non discret les résultats antérieurs dans ce domaine.

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In this paper, we introduce interpolation polynomials on an order of a number field which generalize the usual binomial polynomials. As an application of these polynomials we prove that any entire function on an order of a number field with integer values in this field and which has slow analytic and arithmetic growth is a polynomial. This results extends earlier results in this area to the non discrete case.

     

Classes non ramifiées sur un espace classifiant

In this Note, we establish a general formula for the unramified cohomology of fields of linear invariants by finite groups. Such formulas are known in degree 2 and 3.     

Volumes des représentations sur un corps local

Let be a locally compact second countable group, F a local field of characteristic zero and G an F-almost-simple F-algebraic group. In this paper we study the space X(,G) of Zariski-dense representations : G = G(F) using the natural morphism of cohomological functors * : H*(G, ·) H*(, ·) (where H denotes the continuous cohomology).First let F be a p-adic field. We completely describe the relations between the geometry and the cohomology of G : using geometric properties of the Bruhat-Tits building of G we construct natural cocycles for any irreducible cohomological representation of G. We then adapt these results to the case where the field F is archimedean.Using these cocycles we obtain a simple cohomological characterization of representations with bounded image.Our main result is then the construction, using the previous cocycles and dynamical properties at infinity of , of cohomological invariants (called volumes) on the space X(,G). These volumes describe how the image () goes to infinity in G. They have coefficients in the natural universal infinite-dimensional representation L(, )$\mathbb{C}$ of .In the case where is a cocompact lattice of SO(n, 1) or SU(n, 1), we use these volumes to produce new non-trivial numerical invariants on X(,G), which refine previously known invariants.

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Volumes des représentations sur un corps local

     

Les polynômes orthogonaux de Bergman sur un archipel

Growth estimates for orthogonal polynomials with respect to area measure (Bergman polynomials) over the union of finitely many Jordan regions with piecewise smooth boundary are obtained by a careful investigation of the Green function of the complement, and of Schwarz reflection in analytic arcs of the boundary. As applications we obtain a detailed picture of the limiting zero distribution of Bergman's orthogonal polynomials, and also we propose a robust reconstruction algorithm of the original open set, starting from incomplete data (such as obtained by geometric tomography). To cite this article: B. Gustafsson et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Formes antihermitiennes devenant hyperboliques sur un corps de déploiement

Let H=(a,b)_F be a division quaternion algebra over a field F of characteristic not 2. Denote by τ the canonical involution on H and by K a splitting field of H. If h is a skew-hermitian form over (H,τ) then, by extension of scalars to K and by Morita equivalence, we obtain a quadratic form h_K over K. This gives a map of Witt groups ρ:W⁻¹(H,τ)→W(K) induced by ρ(h)=h_K. When K is a generic splitting field of H we prove in this note that the map ρ is injective.     

Transvecteur de rang 8 sur un corps algébriquement clos

In this Note, we present the classification of trivectors of rank 8 over algebraicallv closed field of arbitrary characteristic by using the arithmetical invariant d_l(w) and the classification of trivectors of lower rank. We determine the maximal length ℓ(K. 8) of the rank-8 trivectors.     

Prolongement analytique des séries de Fourier sur un groupe compact

We study the Fourier series of a central function on a compact simple Lie group. We show that, if its coefficients are interpolated by an analytic function verifying a growth condition, then the sum of the series admits an analytic extension on a domain of the complexified group that in general strictly contains the domain of convergence. This result can be seen as a generalization of a theorem by Lindelöf (see [5], ch. 5).     

Remarks on Completely Regular Lindelöf Reflection of Locales

We prove, under the axiom of countable choice, that the l-ring structure of C(L) of real-valued continuous functions on a locale L determines the completely regular Lindelöf reflection lL of L up to isomorphism. Mathematics Subject Classifications (2000) 54C30, 46E25.Project supported by NSF of China (Grant No. 10271056 and Grant No. 10331011).     

Une remarque sur un théorème de M. Kaczmarz

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Note sur un type d'équations différentielles du premier ordre

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Remarques sur un théorème de M. Fréchet

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Représentation intégrale de fonctionnelles convexes sur un espace de mesures

Résumé Partant d’un résultat abstrait de représentation intègrale pour une fonctionnelle convexe faiblement s.c.i. sur [M _b (Ω)] ^d (obtenu grace à [1]); on établit un résultat de convergence pour une suite de fonctionnelles du type μ _n εM _b ⁺ (Ω),f _n : Ω×R ^d →−∞, +∞] inté Quelques exemples motivés par des applications à la mécanique sont ensuite traités.

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Riassunto Partendo da un risultato astratto di rappresentazione integrale per un funzionale convesso debolmente s.c.i. su [M _b (Ω)] ^d (ottenuto grazie a [1]), si dimostra un risultato di convergenza per una successione di funzionali del tipo con μ _n εM _b ⁺ (Ω),f _n : Ω×R ^d →−∞, +∞] integrando normale convesso. Vengono inoltre trattati alcuni esempi motivati da applicazioni alla Meccanica.