Dynamics of the Volterra-Type Integral and Differentiation Operators on Generalized Fock Spaces

被引：5

作者：

Bonet, Jose ^{[1
]}

Mengestie, Tesfa ^{[2
]}

Worku, Mafuz ^{[3
]}

机构：

[1] Univ Politecn Valencia, IUMPA, Valencia 46071, Spain

[2] Western Norway Univ Appl Sci, Dept Math Sci, Klingenbergvegen 8, N-5414 Stord, Norway

[3] Addis Ababa Univ, Dept Math, Addis Ababa, Ethiopia

来源：

RESULTS IN MATHEMATICS | 2019年 / 74卷 / 04期

关键词：

Generalized Fock spaces; power bounded; uniformly mean ergodic; Volterra-type integral operator; differential operator; Hardy operator; supercyclic; hypercyclic; cyclic; Ritt's resolvent condition; WEIGHTED BANACH-SPACES;

D O I：

10.1007/s00025-019-1123-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Various dynamical properties of the differentiation and Volterra-type integral operators on generalized Fock spaces are studied. We show that the differentiation operator is always supercyclic on these spaces. We further characterize when it is hypercyclic, power bounded and uniformly mean ergodic. We prove that the operator satisfies the Ritt's resolvent condition if and only if it is power bounded and uniformly mean ergodic. Some similar results are obtained for the Volterra-type and Hardy integral operators.

引用

页数：15

共 30 条

[1] Differentiation and integration operators on weighted Banach spaces of holomorphic functions [J].