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February  2005, 13(2): 271-275. doi: 10.3934/dcds.2005.13.271

On a hypercylicity criterion for strongly continuous semigroups

Samir EL Mourchid 1,

1. 

Département de Mathématiques, Université Cadi Ayyad, Marrakech, B.P.: 2390, Morocco

Received  March 2004 Revised  January 2005 Published  April 2005

In this note we extend the hypercyclicity criterion (HC) to $C_0$- semigroups on separable Banach spaces and characterize semigroups satisfying (HC). Using (HC) we show the hypercyclicity of the translation group on the weighted spaces $L^p_\rho(\mathbb R,\mathbb C)$ or $C_{0,\rho}(\mathbb R,\mathbb C)$ for admissible weight functions $\rho$.
Keywords: hypercyclicity criterion, Hypercyclic semigroups, topologically transitive.
Mathematics Subject Classification: 47A16, 47D06, 47B37.
Citation: Samir EL Mourchid. On a hypercylicity criterion for strongly continuous semigroups. Discrete & Continuous Dynamical Systems, 2005, 13 (2) : 271-275. doi: 10.3934/dcds.2005.13.271
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