algebras and the symbolic calculus of Sebastião e Silva. (Les algèbres et le calcul symbolique de Sebastião e Silva.)
Absolute bases, tensor products and a theorem of Bohr
Analytic functions on c0.
Approximation of holomorphic functions of infinitely many variables II
Let be a Banach space and the ball of radius centered at . Can any holomorphic function on be approximated by entire functions, uniformly on smaller balls ? We answer this question in the affirmative for a large class of Banach spaces.
Approximation of holomorphic mappings on infinite dimensional spaces.
In this article we examine necessary and sufficient conditions for the predual of the space of holomorphic mappings of bounded type, Gb(U), to have the approximation property and the compact approximation property and we consider when the predual of the space of holomorphic mappings, G(U), has the compact approximation property. We obtain also similar results for the preduals of spaces of m-homogeneous polynomials, Q(mE).
Bolzano’s intermediate-value theorem for quasi-holomorphic maps
We extend Bolzano’s intermediate-value theorem to quasi-holomorphic maps of the space of continuous linear functionals from l p into the scalar field, (0< p<1). This space is isomorphic to l ∞.
Complementation in spaces of symmetric tensor products and polynomials.
Our aim here is to announce some properties of complementation for spaces of symmetric tensor products and homogeneous continuous polynomials on a locally convex space E that have, in particular, consequences in the study of the property (BB)n,s recently introduced by Dineen [8].
Construction of Sobolev spaces of fractional order with sub-riemannian vector fields
Given a smooth family of vector fields satisfying Chow-Hörmander’s condition of step 2 and a regularity assumption, we prove that the Sobolev spaces of fractional order constructed by the standard functional analysis can actually be “computed” with a simple formula involving the sub-riemannian distance.Our approach relies on a microlocal analysis of translation operators in an anisotropic context. It also involves classical estimates of the heat-kernel associated to the sub-elliptic Laplacian.
Convolution operators in infinite dimension.
Countable sets of holomorphic mappings
Distinguished preduals of spaces of holomorphic functions.
Dualidad y extensiones en holomorfía infinita
ELB holomorphic factorization over projective limit representations
Entire functions uniformly bounded on balls of a Banach space
Let X be an infinite-dimensional complex Banach space. Very recently, several results on the existence of entire functions on X bounded on a given ball B₁ ⊂ X and unbounded on another given ball B₂ ⊂ X have been obtained. In this paper we consider the problem of finding entire functions which are uniformly bounded on a collection of balls and unbounded on the balls of some other collection.
Extension of smooth functions in infinite dimensions II: manifolds
Let M be a separable Finsler manifold of infinite dimension. Then it is proved, amongst other results, that under suitable conditions of local extensibility the germ of a function, or of a section of a vector bundle, on the union of a closed submanifold and a closed locally compact set in M, extends to a function on the whole of M.
Factorization of weakly continuous holomorphic mappings
We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly continuous on weakly bounded sets if and only if it is weakly uniformly} continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Hervés and Valdivia for polynomials between Banach spaces, and it also holds if the weak topology is replaced by a coarser...
Hilbert spaces of analytic functions of infinitely many variables
We study spaces of analytic functions generated by homogeneous polynomials from the dual space to the symmetric Hilbertian tensor product of a Hilbert space. In particular, we introduce an analogue of the classical Hardy space H² on the Hilbert unit ball and investigate spectral decomposition of unitary operators on this space. Also we prove a Wiener-type theorem for an algebra of analytic functions on the Hilbert unit ball.
Holomorphic functions and Banach-nuclear decompositions of Fréchet spaces
We introduce a decomposition of holomorphic functions on Fréchet spaces which reduces to the Taylor series expansion in the case of Banach spaces and to the monomial expansion in the case of Fréchet nuclear spaces with basis. We apply this decomposition to obtain examples of Fréchet spaces E for which the τ_{ω} and τ_{δ} topologies on H(E) coincide. Our result includes, with simplified proofs, the main known results-Banach spaces with an unconditional basis and Fréchet nuclear spaces with DN [2,...
Holomorphic Functions and the (BB)-Property.
Holomorphic functions on Fréchet spaces with Schauder basis.