The Spaces of Analytic Functions on Open Subsets of and

  • José M. Ansemil

    Universidad Complutense de Madrid, Spain
  • Jerónimo López-Salazar

    Universidad Politécnica de Madrid, Spain
  • Socorro Ponte

    Universidad Complutense de Madrid, Spain

Abstract

This paper is devoted to study the space of all analytic functions on an open subset of or . It is proved that if satisfies a weak condition (that will be called 0-property), then every depends only on a finite number of variables. Then several topologies on are studied: the compact open topology, the topology (already known in spaces of holomorphic functions) and a new one, defined by the inductive limit of the subspaces of analytic functions which only depend on the first variables.

Cite this article

José M. Ansemil, Jerónimo López-Salazar, Socorro Ponte, The Spaces of Analytic Functions on Open Subsets of and . Publ. Res. Inst. Math. Sci. 51 (2015), no. 1, pp. 191–206

DOI 10.4171/PRIMS/152