Characterizations of the linear topological invariants and the solutions to some problems of holomorphic functions (Q1030970)

From the author's 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, \(\delta-\)separately holomorphic functions, 4. \(\sigma(\cdot,W)-\)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.