Complex Analysis and Operator Theory

, Volume 13, Issue 2, pp 341–349 | Cite as

Weighted Inductive Limits of Holomorphic Functions with o-Growth Condition

  • Alexander V. AbaninEmail author
  • Pham Trong Tien


We study topological properties of weighted (LB)-spaces of holomorphic functions on open sets with o-growth condition. We show that such spaces are semi-Montel if and only if they are (DFS). We also establish that, for a wide family of open sets, some important topological properties of such holomorphic spaces are always equivalent and necessary for a space to be equal algebraically to its projective hull. This means, in particular, that for such open sets these spaces behave in a very similar way as the corresponding spaces of continuous functions.


Weighted function spaces Weighted inductive limits Growth conditions 

Mathematics Subject Classification

Primary 46E10 30H05 46A13 



This note was written when the second author visited the Department of Applied Mathematics at the University of Washington. He would like to thank the Department and Professor Aleksandr Aravkin for the hospitality.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Southern Mathematical InstituteVladikavkazRussian Federation
  2. 2.Southern Federal UniversityRostov-on-DonRussian Federation
  3. 3.Hanoi University of Science, Vietnam National UniversityHanoiVietnam

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