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Complex Analysis and Operator Theory

, Volume 11, Issue 3, pp 611–626 | Cite as

Tensor Representation of Spaces of Holomorphic Functions and Applications

  • Thai Thuan Quang
  • Duong Quoc Huy
  • Duong Thanh Vy
Article

Abstract

In this paper we study the tensor representation of spaces of Fréchet-valued holomorphic functions \([H(U, F),\tau ]\) in the form \( [(H(U), \tau )] \widehat{\otimes }_{\pi }F\) where U is an open subset of a Fréchet space and \(\tau \in \{\tau _0, \tau _\omega , \tau _\delta \}.\) Using this result we consider the following problems: exponential laws for the topologies \(\tau _0, \tau _\omega \) on the space \(H(U \times V)\) where U and V are two open subsets of locally convex spaces E and F respectively; the coincidence of the topologies \(\tau _0, \tau _\omega , \tau _\delta \) on spaces of locally convex valued holomorphic functions (resp. germs) H(UF) [resp. H(KF)]; the inheritance of the properties (QNo),  \((QNo)'\) via the spaces of holomorphic functions and of holomorphic germs.

Keywords

Infinite-dimensional holomorphy Topological tensor products Fréchet spaces and (DF)-spaces 

Mathematics Subject Classification

46G20 36A32 46A04 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Thai Thuan Quang
    • 1
  • Duong Quoc Huy
    • 2
  • Duong Thanh Vy
    • 1
  1. 1.Department of MathematicsQuy Nhon UniversityBinh DinhVietnam
  2. 2.Department of Natural Science and TechnologyTay Nguyen UniversityDak LakVietnam

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