Let G be an open subset of C and let V be an arbitrary system of weights on G: Let HVb(G) and HV0(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 HVb(G) and HV0(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 operatos.
- Weighted locally convex spaces of holomorphic functions
- arbitrary system of weights
- dynamical systems
- invertible multiplication operators
- multiplication operators
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