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On real analytic functions of unbounded type


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.

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The second author has been supported by Universidad Complutense de Madrid, grant BE45/08.

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Correspondence to J. M. Ansemil.

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Ansemil, J.M., López-Salazar, J. & Ponte, S. On real analytic functions of unbounded type. Rev Mat Complut 26, 549–560 (2013).

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  • Banach space
  • Analytic function

Mathematics Subject Classification (2000)

  • 46E10
  • 46E50