**J. S. Manhas**

## Multiplication Operators and Dynamical Systems on
Weighted Locally Convex

Spaces of Holomorphic Functions

**Abstract:**

Let $G$ be an open subset of $\mathbb{C}$ and let $V$ be an arbitrary system of
weights on $G.$ Let $HV_{b}(G)$ and $HV_{0}(G)$ be the weighted locally convex
spaces of holomorphic functions with a topology generated by seminorms which are
weighted analogues of the supremum norm. In the present article, we characterize
the analytic functions inducing multiplication operators and invertible
multiplication operators on the spaces $HV_{b}(G)$ and $HV_{0}(G)$ for different
systems of weights $V$ on $G$. A (linear) dynamical system induced by
multiplication operators on these spaces is obtained as an application of the
theory of multiplication operators.

**Keywords:**

Weighted locally convex spaces of holomorphic functions, arbitrary system of
weights, seminorms, multiplication operators, invertible multiplication
operators, dynamical systems.

**MSC 2000:** Primary: 47B37, 47B38, 46E10; secondary: 47D03, 37B05, 32A10,
30H05.