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Holomorphy in convergence spaces

Abstract

We introduce a new approach to infinite dimensional holomorphy. Cast in the setting of closed-embedded linear convergence spaces and based on a categorical definition of derivative, our theory applies beyond the traditional open domains. It reaches certain domains with empty interior (that arise naturally in Fréchet spaces) and gives a fully fledged differential calculus. On open domains our approach provides a new characterization of holomorphic maps. Thus earlier theories become expanded as well as strengthened.

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Monadi, A., Nel, L.D. Holomorphy in convergence spaces. Appl Categor Struct 1, 233–245 (1993). https://doi.org/10.1007/BF00880045

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Mathematics Subject Classifications (1991)

  • Primary: 46G20
  • Secondary: 58B12, 46M40

Key words

  • Infinite dimensional holomorphy
  • closed-embedded linear convergence spaces
  • analyte
  • categorical methods
  • categorical differentiation theory