Vietnam
Journal of Mathematics 37:2&3 (2009) 357378

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 Fréchetvalued holomorphic
functions,

3. Weakly holomorphic functions, δ separately holomorphic
functions,

4. σ(., W)holomorphic functions and theorems of
Vitalitype,

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.
