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Vietnam Journal of Mathematics 37:2&3 (2009) 357-378 

Characterizations of the Linear Topological Invariants and the Solutions to some Problems of Holomorphic Functions

Thai Thuan Quang

Abstract.  The theory of holomorphic functions between locally convex spaces having linear topological invariants has attracted the attention of many researchers during the last thirty years. This report is a survey about recent results of the following problems from this theory:

1. Locally bounded holomorphic functions,

2. The regularity of spaces of germ of Fréchet-valued holomorphic functions,

3. Weakly holomorphic functions, δ- separately holomorphic functions,

4. σ(., W)-holomorphic functions and theorems of Vitali-type,

5. The exponential representation of holomorphic functions and absolute representation system,

6. Separately holomorphic functions,

7. Holomorphic functions of uniformly bounded type on tensor products.

2000 Mathematics Subject Classification: 32A10, 32B10, 46A04, 46E50, 46A63, 30B50.

Keywords: Holomorphic functions, Holomorphic functions of uniform type, Topological linear invariants, Exponential representation.

 

 

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