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If E and F are complex Banach spaces, and fixing a balanced open subset U of E, we let Hb=(Hb(U;F),?b) denote the space of all mappings f:U?F which are holomorphic of bounded type, endowed with its natural topology ?b; clearly, Hb is a Fréchet s[...]texto impreso
Let f be a holomorphic function on a complex normed space E. The possibility of extending f to the completion of E has been studied by Hirschowitz, Noverraz, Dineen, and Dineen-Noverraz. Here, following the ideas in [4, section 6.1], we study th[...]texto impreso
Let f be a holomorphic function on a complex normed space E. The possibility of extending f to the completion of E has been studied by Hirschowitz, Noverraz, Dineen, and Dineen-Noverraz. Here, following the ideas in [4, section 6.1], we study th[...]texto impreso
Ansemil, José María M. ; Blasco Contreras, Fernando ; Ponte, Socorro | Suomalainen tiedeakatemia | 2000In this paper we point out some relations concerning properties (BB)(n) and (BB)(n,s) related to the "Probleme des topologies" of Grothendieck and give a first example of a Frechet space with the (BB)(2) property but without the (BB)(3) property.texto impreso
In this paper we prove that given any two disjoint balls in an infinite dimensional complex Banach space, there exists an entire function which is bounded on one and unbounded on the other.texto impreso
J.-F. Colombeau and S. Ponte [same journal 5 (1982), no. 2, 123–135;] defined and studied a dense linear subspace E(E) (with a stronger complete locally convex topology) of the space E(E) of all (Silva) C^?-functions on a real nuclear bornologic[...]texto impreso
Let E be a DFN space, E' its strong topological dual, H(E) and H(E') the corresponding spaces of holomorphic functions from E and E' into endowed with the respective compact-open topologies and Exp E' the vector subspace of H(E') consisting of t[...]texto impreso
Let U be an open subset of a complex locally convex space E, let F be a closed subspace of E, and let PI:E --> E/F be the canonical quotient mapping. In this paper we study the induced mapping PI*, taking f is-an-element-of H(b)(PI(U))--> f ci[...]texto impreso
Ansemil, José María M. ; López-Salazar Codes, Jerónimo ; Ponte, Socorro | Polish Acad Sciencies Inst Mathematics | 2011Let 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 B(1) subset of X and unbounded on another given ball B(2) subset of X have been obtained. In [...]texto impreso
In this work we investigate the inverse approximation problems in the Lebesgue and Smirnov spaces with weights satisfying the so-called Muckenhoupt's Ap condition in terms of the -th mean modulus of smoothness, > 0. We obtain a converse theore[...]texto impreso
In this note we prove that for Fréchet spaces with a basis, the locally determining sets at O for analytic functions in a wide class have a null sequence which is also locally determining at O for analytic functions. This gives a partial answer [...]texto impreso
A subset L of a complex locally convex space E is said to be locally determining at 0 for holomorphic functions if for every connected open 0-neighborhood U and every f?H(U), whenever f vanishes on U?L, then f?0. The authors' main result is that[...]texto impreso
In this paper we prove, among other things, that the space of all holomorphic functions on an open subset U of a complex metrizable space E, endowed with the Nachbin ported topology, is metrizable only if E has finite dimension. This answers a q[...]texto impreso
The authors solve an interesting open problem concerning the equivalence of the compact-open topology ?0 and the Nachbin ported topology ?? on spaces of holomorphic functions. (See, for example, the book by S. Dineen [Complex analysis in locally[...]texto impreso
In this paper we prove several results on the existence of analytic functions on an infinite dimensional real Banach space which are bounded on some given collection of open sets and unbounded on others. In addition, we also obtain results on th[...]
