Espaces tonnelé, infra-tonnelé et -tonnelé
Bornological and Ultrabornological C(X;E) Spaces.
The Zahorski theorem is valid in Gevrey classes
Let Ω,F,G be a partition of such that Ω is open, F is and of the first category, and G is . We prove that, for every γ ∈ ]1,∞[, there is an element of the Gevrey class Γγ which is analytic on Ω, has F as its set of defect points and has G as its set of divergence points.
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.
On nuclear maps between spaces of ultradiferentiables jets of Roumieu type.
Si K es un compacto no vacío en R, damos una condición suficiente para que la inyección canónica de ε(K) en ε(K) sea nuclear. Consideramos el caso mixto y obtenemos la existencia de un operador de extensión nuclear de ε(F) en ε(R) donde F es un subconjunto cerrado propio de R y A y D son discos de Banach adecuados. Finalmente aplicamos este último resultado al caso Borel, es decir cuando F = {0}.
Holomorphic extension maps for spaces of Whitney jets.
The key result (Theorem 1) provides the existence of a holomorphic approximation map for some space of C-functions on an open subset of R. This leads to results about the existence of a continuous linear extension map from the space of the Whitney jets on a closed subset F of R into a space of holomorphic functions on an open subset D of C such that D ∩ R = RF.
Mixed intersections of non quasi-analytic classes.
Analytic extension of ultradifferentiable Whitney jets.
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].
Sur les espaces bornologiques
Page 1