Información del autor
Autor Ansemil, José María M. |
Documentos disponibles escritos por este autor (33)
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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.![]()
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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.![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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 [...]![]()
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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[...]![]()
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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 [...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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Let E be a complex locally convex space, U a balanced open subset of E. The author continues the study of the quasinormability of the space Hb(U) of all holomorphic functions on U which are bounded on the U-bounded subsets of U. His main goal is[...]![]()
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Ansemil, José María M. ; Blasco Contreras, Fernando ; Ponte, Socorro | Università del Salento | 1997A property P of locally convex spaces is called a three-space property whenever the following implication holds: if both a closed subspace F and the corresponding quotient E/F of a locally convex space E have P then E has P as well. The authors [...]![]()
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Properties (BB)n, n = 2, 3, ... on a locally convex space (see the definition below) have been recently introduced ([10]). They are interesting, among other things, in connection with the study of natural topologies on spaces of polynomials, mul[...]![]()
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An example of a Frechet space E is given such that the space of n-homogeneous continuous polynomials on E, endowed with any of the natural topologies usually considered on it, is quasinormable for every n is an element of N. This space has the p[...]![]()
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Let E be a Fréchet space and p( n E) the space of n-homogeneous continuous polynomials on E, endowed with topology ? b of uniform convergence on the bounded subsets of E. The author gives an example of a Fréchet space E such that (p( n E),? b ) [...]![]()
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In this paper we give a survey on recent results concerning the coincidence or not of the compact-open and the Nachbin ported topologies on the space of all holomorphic functions on an open subset of a complex Fréchet space.'![]()
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Ansemil, José María M. ; Aron, Richard M. ; Ponte, Socorro | European Mathematical Society | 2009-06We prove the impossibility of expressing the space of entire functions on any infinite dimensional complex Banach space with a Schauder basis E as a countable union of spaces of entire functions that are bounded on countable open covers of E.![]()
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Ansemil, José María M. ; Ponte, Socorro | Real Academia de Ciencias Exactas, Físicas y Naturales | 2000This informative paper surveys applications of results in the theory of topological tensor products of Fréchet or (DF)-spaces to the topological structure of spaces of n-homogeneous continuous polynomials. Recent progress about tensor products w[...]![]()
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Let E be a complex locally convex space, F a closed subspace, and let ? be the canonical quotient mapping from E onto E/F. Let H(U) [resp. H(K)] be the set of holomorphic functions on the open set U of E [resp. the set of germs of holomorphic fu[...]![]()
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Let (X, ?) be a Riemann domain over a complex Fréchet space E, K a compact subset of X and (K) the vector space of all holomorphic germs on K. Given an F-quotient (XF, ?F, ?) of (X, ?) (see the definition below), the canonical mapping ? : X ? X[...]![]()
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Here we show how, in the general context of locally convex spaces, it is possible to get an n-tensor topology (on spaces of n-tensor products) from an n-tensor topology on spaces of symmetric n-tensors products. Indeed, given an n-tensor topolog[...]![]()
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Let H(U) be the space of holomorphic functions on an open subset U of a complex locally convex space E, and let H(K) be the space of holomorphic germs on a compact subset K of E. (For background on holomorphic functions on locally convex spaces [...]![]()
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The authors are concerned with the characterization of those functions holomorphic on EC? which are Fourier transforms of elements of ?? (E). Here E is a complete bornological vector space over R, ? (E) stands for the space of all complex-valued[...]![]()
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Ansemil, José María M. ; Ponte, Socorro ; López-Salazar Codes, Jerónimo | European Mathematical Society | 2015This paper is devoted to studying the space A(U) of all analytic functions on an open subset U of ?? or ??. It is proved that if U satisfies a weak condition (that will be called the 0-property), then every f ? A(U) depends only on afinite numbe[...]![]()
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An explicit representation of the n-fold symmetric tensor product (equipped with a natural topology tau such as the projective, injective or inductive one) of the finite direct sum of locally convex spaces is presented. The formula for circle ti[...]![]()
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By a classical theorem, there is an isomorphism between the space of entire functions of exponential type on Cn,ExpCn, and the analytic functions on H(Cn),H?(Cn) [see, for example, F. Trèves, Topological vector spaces, distributions, and kernels[...]![]()
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Let H(U) be the space of holomorphic functions on an open subset U of a locally convex space. The authors study various topologies canonically associated with the topology of compact convergence on H(U), especially the bornological topology and [...]![]()
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Sean, U un abierto equilibrado de un espacio localmente convexo complejo E, H(U) el espacio vectorial de las funciones holomorfas en U y to y tw las topologías compacto-abierta y portada de Nachbin respectivamente en H(U). Se prueba en esta nota[...]