caa a22 4500 46793200X CHVBK 20180406152946.0 cr unu---uuuuu 170328e20061001xx s 000 0 eng 10.1007/s00020-006-1423-7 doi (NATIONALLICENCE)springer-10.1007/s00020-006-1423-7 On a Theorem of Godefroy and Shapiro [Elektronische Daten] [A. Bonilla, K. Grosse-Erdmann] Abstract.: G. Godefroy and J. H. Shapiro have shown that every operator on $$ H(\mathbb{C}^{N} ),\; N \geq 1 $$ , that commutes with all translation operators $$ T_{a} f(z) = f(z + a),\; a \in \mathbb{C}^{N} $$ , and that is not a scalar multiple of the identity is hypercyclic. We show that they are even frequently hypercyclic. In addition, we obtain growth conditions that may be satisfied by corresponding frequently hypercyclic entire functions. Birkhäuser Verlag, Basel, 2006 Frequently hypercyclic operator nationallicence infinite order differential operator nationallicence rate of growth of entire function nationallicence Bonilla A. Departamento de Análisis Matemático, Universidad de La Laguna, 38271, La Laguna (Tenerife), Spain aut Grosse-Erdmann K. Fachbereich Mathematik, FernUniversität Hagen, D-58084, Hagen, Germany aut Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhäuser.ch 56/2(2006-10-01), 151-162 0378-620X 56:2<151 2006 56 20 https://doi.org/10.1007/s00020-006-1423-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00020-006-1423-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bonilla A. Departamento de Análisis Matemático, Universidad de La Laguna, 38271, La Laguna (Tenerife), Spain aut NATIONALLICENCE 700 1- Grosse-Erdmann K. Fachbereich Mathematik, FernUniversität Hagen, D-58084, Hagen, Germany aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhäuser.ch 56/2(2006-10-01), 151-162 0378-620X 56:2<151 2006 56 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer