Chaos of the Differentiation Operator on Weighted Banach Spaces of Entire Functions

被引：0
作者：
José Bonet
Antonio Bonilla
机构：
[1] Universidad Politécnica de Valencia,Instituto Universitario de Matemática, Pura y Aplicada IUMPA
[2] Universidad de La Laguna,Departamento de Análisis Matemático
来源：
Complex Analysis and Operator Theory | 2013年 / 7卷
关键词：
Weighted spaces of entire functions; Differentiation operator; Hypercyclic operator; Chaotic operator; Frequently hypercyclic operator; Primary 47A16; Secondary 46E15; 47B38;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Motivated by recent work on the rate of growth of frequently hypercyclic entire functions due to Blasco, Grosse-Erdmann and Bonilla, we investigate conditions to ensure that the differentiation operator is chaotic or frequently hypercyclic on generalized weighted Bergman spaces of entire functions studied by Lusky, whenever the differentiation operator is continuous. As a consequence we partially complete the knowledge of possible rates of growth of frequently hypercyclic entire functions for the differentiation operator.
引用
收藏
页码：33 / 42
页数：9
相关论文
共 29 条
[1]  
Bayart F.(2004)Hypercyclicité: le rôle du spectre ponctuel unimodulaire C. R. Math. Acad. Sci. Paris 338 703-708
[2]  
Grivaux S.(2006)Frequently hypercyclic operators Trans. Am. Math. Soc. 358 5083-5117
[3]  
Bayart F.(2002)Exponential type of hypercyclic entire functions Arch. Math. (Basel) 78 283-290
[4]  
Grivaux S.(1993)Weighted spaces of holomorphic functions on balanced domains Mich. Math. J. 40 271-297
[5]  
Bernal-Gonz alez L.(2010)Rate of growth of frequently hypercyclic functions Proc. Edinburgh Math. Soc. 53 39-59
[6]  
Bonilla A.(2006)On a theorem of Godefroy and Shapiro Integr. Equa. Oper. Theory 56 151-162
[7]  
Bierstedt K.D.(2007)Frequently hypercyclic operators and vectors, Ergodic Theory Dynam Systems 29 383-404
[8]  
Bonet J.(2009)Dynamics of the differentiation operator on weighted spaces of entire functions Math. Z. 261 649-657
[9]  
Galbis A.(1990)On the universal functions of G. R. MacLane Complex Variables Theory Appl. 15 193-196
[10]  
Blasco O.(1999)Universal families and hypercyclic operators Bull. Am. Math. Soc. (N.S.) 36 345-381
123