p-adic Ascoli theorems.
The aim of this paper is the study of a certain class of compact-like sets within some spaces of continuous functions over non-Archimedean ground fields. As a result, some p-adic Ascoli theorems are obtained.
P-adic Spaces of Continuous Functions I
Properties of the so called -complete topological spaces are investigated. Also, necessary and sufficient conditions are given so that the space of all continuous functions, from a zero-dimensional topological space to a non-Archimedean locally convex space , equipped with the topology of uniform convergence on the compact subsets of to be polarly barrelled or polarly quasi-barrelled.
Partial differential operators of infinite order with constant coefficients on the space of analytic functions on the polydisc
Parties bornées d'un espace topologique complètement régulier
Partition continue de l'unite et C-repletion.
Perfect sets of finite class without the extension property
We prove that generalized Cantor sets of class α, α ≠ 2 have the extension property iff α < 2. Thus belonging of a compact set K to some finite class α cannot be a characterization for the existence of an extension operator. The result has some interconnection with potential theory.
Points extrémaux dans certains cônes convexes
Polynomials and multilinear mappings in topological vector-spaces
Positive vector measures with given marginals
Suppose is an ordered locally convex space, and Hausdorff completely regular spaces and a uniformly bounded, convex and closed subset of . For , let . Then, under some topological and order conditions on , necessary and sufficient conditions are established for the existence of an element in , having marginals and .
Prevalence of "nowhere analyticity"
This note brings a complement to the study of genericity of functions which are nowhere analytic mainly in a measure-theoretic sense. We extend this study to Gevrey classes of functions.
Problèmes d'analyticité pour des opérateurs différentiels dégénérés ; applications (suite)
Problèmes d'analyticité pour des opérateurs différentiels dégénérés ; applications
Problèmes d'analyticité pour des opérateurs différentiels dégénérés ; applications (fin)
Problèmes de Cauchy globaux
Problèmes d'interpolation dans quelques espaces de fonctions non entières
Problèmes généraux de prolongement des fonctions dérivables
Projective representations of spaces of quasianalytic functionals
The weighted inductive limit of Fréchet spaces of entire functions in N variables which is obtained as the Fourier-Laplace transform of the space of analytic functionals on an open convex subset of can be described algebraically as the intersection of a family of weighted Banach spaces of entire functions. The corresponding result for the spaces of quasianalytic functionals is also derived.
Pseudodifferential operators on non-quasianalytic classes of Beurling type
We introduce pseudodifferential operators (of infinite order) in the framework of non-quasianalytic classes of Beurling type. We prove that such an operator with (distributional) kernel in a given Beurling class is pseudo-local and can be locally decomposed, modulo a smoothing operator, as the composition of a pseudodifferential operator of finite order and an ultradifferential operator with constant coefficients in the sense of Komatsu, both operators with kernel in the same class . We also...