Entire functions on locally convex spaces and convolution operators
Entire functions on nuclear sequence spaces.
Errata to: Local Mappings on Spaces of Differentiable Functions [1].
Espaces associés aux espaces linéaires à semi-normes des fonctions continues et bornées sur un espace complètement régulier et séparé
Espaces tonnelé, infra-tonnelé et -tonnelé
Espaces de Riesz, espaces de fonctions et espaces de sections
Espaces fortement réticulés de fonctions affines
Espaces uniformes et espaces de mesures
Espacios de funciones holomorfas cuyas diferenciales se extienden en el origen.
Estimates in Sobolev norms for harmonic and holomorphic functions and interpolation between Sobolev and Hölder spaces of harmonic functions
Étude des projections de norme 1 de sur . Unicité de certains préduaux. Applications
On étudie dans ce travail les projections de norme 1 du bidual d’un espace de Banach sur l’image canonique de dans . On montre que dans un certain nombre de cas, il y a unicité de la projection de norme 1. On en déduit des théorèmes d’existence et d’unicité du prédual de . On donne ensuite diverses applications, en particulier aux espaces dont la norme est différentiable sur un ensemble dense et aux espaces ne contenant pas .
Explicit extension maps in intersections of non-quasi-analytic classes
We deal with projective limits of classes of functions and prove that: (a) the Chebyshev polynomials constitute an absolute Schauder basis of the nuclear Fréchet spaces ; (b) there is no continuous linear extension map from into ; (c) under some additional assumption on , there is an explicit extension map from into by use of a modification of the Chebyshev polynomials. These results extend the corresponding ones obtained by Beaugendre in [1] and [2].
Extended composition operators in weighted spaces.
Extension Gevrey et rigidité dans un secteur
We study a rigidity property, at the vertex of some plane sector, for Gevrey classes of holomorphic functions in the sector. For this purpose, we prove a linear continuous version of Borel-Ritt's theorem with Gevrey conditions
Extension maps in ultradifferentiable and ultraholomorphic function spaces
The problem of the existence of extension maps from 0 to ℝ in the setting of the classical ultradifferentiable function spaces has been solved by Petzsche [9] by proving a generalization of the Borel and Mityagin theorems for -spaces. We get a Ritt type improvement, i.e. from 0 to sectors of the Riemann surface of the function log for spaces of ultraholomorphic functions, by first establishing a generalization to some nonclassical ultradifferentiable function spaces.
Extension operators for analytic functions defined on certain closed subvarieties of a Stein space
Extension via interpolation
We suggest a modification of the Pawłucki and Pleśniak method to construct a continuous linear extension operator by means of interpolation polynomials. As an illustration we present explicitly the extension operator for the space of Whitney functions given on the Cantor ternary set.
Extensions de jets dans des intersections de classes non quasi-analytiques
In [3], J. Chaumat and A.-M. Chollet prove, among other things, a Whitney extension theorem, for jets on a compact subset E of ℝⁿ, in the case of intersections of non-quasi-analytic classes with moderate growth and a Łojasiewicz theorem in the regular situation. These intersections are included in the intersection of Gevrey classes. Here we prove an extension theorem in the case of more general intersections such that every -Whitney jet belongs to one of them. We also prove a linear extension theorem...
Extensions of compact continuous maps into decomposable sets
Facial Topologies for Subspaces of C(X).