On real analytic functions of unbounded type.
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2013
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Martínez Ansemil, J. M., López-Salazar Codes, J. & Ponte Miramontes, M. S. «On Real Analytic Functions of Unbounded Type». Revista Matemática Complutense, vol. 26, n.o 2, julio de 2013, pp. 549-60. DOI.org (Crossref), https://doi.org/10.1007/s13163-012-0095-x.
Abstract
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 the density of some subsets of the space of all analytic functions for natural locally convex topologies on this space