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Common hypercyclic functions for multiples of convolution and non-convolution operators
Author(s):
Luis
Bernal-González
Journal:
Proc. Amer. Math. Soc.
137
(2009),
3787-3795.
MSC (2000):
Primary 47A16;
Secondary 30E10, 47B33
Posted:
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  , where  is the differential operator associated to an entire function of order less than  . The same result holds if  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:
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
Posted:
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
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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