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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Common hypercyclic functions for multiples of convolution and non-convolution operators


Author: Luis Bernal-González
Journal: Proc. Amer. Math. Soc. 137 (2009), 3787-3795
MSC (2000): Primary 47A16; Secondary 30E10, 47B33
Published electronically: June 5, 2009
MathSciNet review: 2529888
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Abstract: We prove the existence of a residual set of entire functions, all of whose members are hypercyclic for every non-zero scalar multiple of $ T$, where $ T$ is the differential operator associated to an entire function of order less than $ 1/2$. The same result holds if $ T$ is a finite-order linear differential operator with non-constant coefficients.


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Additional Information

Luis Bernal-González
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, Avda. Reina Mercedes, Sevilla-41080, Spain
Email: lbernal@us.es

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09943-2
PII: S 0002-9939(09)09943-2
Keywords: Hypercyclic operators, common hypercyclic vectors, entire functions, linear differential operators, Borel transform
Received by editor(s): July 7, 2008
Received by editor(s) in revised form: February 23, 2009
Published electronically: June 5, 2009
Additional Notes: The author has been partially supported by the Plan Andaluz de Investigación de la Junta de Andalucía FQM-127, by MEC Grant MTM2006-13997-C02-01 and by MEC Acción Especial MTM2006-26627-E
Dedicated: Dedicated to the memory of Professor Antonio Aizpuru, who died in March 2008
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.