### Abstract

Let G be an open subset of 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 operatos.

Original language | English |
---|---|

Pages (from-to) | 527-537 |

Number of pages | 11 |

Journal | Georgian Mathematical Journal |

Volume | 11 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2004 |

### Fingerprint

### 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

**Multiplication operators and dynamical systems on weighted locally convex spaces of holomorphic functions.** / Manhas, J. S.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Multiplication operators and dynamical systems on weighted locally convex spaces of holomorphic functions

AU - Manhas, J. S.

PY - 2004

Y1 - 2004

N2 - 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.

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.

KW - arbitrary system of weights

KW - dynamical systems

KW - invertible multiplication operators

KW - multiplication operators

KW - seminorms

KW - Weighted locally convex spaces of holomorphic functions

UR - http://www.scopus.com/inward/record.url?scp=80051594964&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80051594964&partnerID=8YFLogxK

U2 - 10.1515/GMJ.2004.527

DO - 10.1515/GMJ.2004.527

M3 - Article

VL - 11

SP - 527

EP - 537

JO - Georgian Mathematical Journal

JF - Georgian Mathematical Journal

SN - 1572-9176

IS - 3

ER -