Multiplication operators and dynamical systems on weighted locally convex spaces of holomorphic functions

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2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)527-537
Number of pages11
JournalGeorgian Mathematical Journal
Volume11
Issue number3
DOIs
Publication statusPublished - 2004

Fingerprint

Multiplication Operator
Locally Convex Space
Weighted Spaces
Analytic function
Dynamical system
Linear Dynamical Systems
G-space
Seminorm
Supremum
Invertible
Multiplication
Analogue
Topology
Norm
Subset
Arbitrary

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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AB - 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.

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KW - seminorms

KW - Weighted locally convex spaces of holomorphic functions

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