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F. Bayart, S. Grivaux, R. Mortini (2008)
Common bounded universal functions for composition operatorsIllinois Journal of Mathematics, 52
Kit Chan, Rebecca Sanders (2011)
Common Hypercyclic Vectors for the Conjugate Class of a Hypercyclic OperatorJournal of Mathematical Analysis and Applications, 375
N. Tsirivas (2014)
Common hypercyclic functions for translation operators with large gaps IIarXiv: Functional Analysis
J. Conejero, V. Müller, A. Peris (2007)
Hypercyclic behaviour of operators in a hypercyclic C 0 -semigroupJournal of Functional Analysis, 244
F. Bayart, É. Matheron (2007)
How to get common universal vectorsIndiana University Mathematics Journal, 56
N. Tsirivas (2014)
EXISTENCE OF COMMON HYPERCYCLIC VECTORS FOR TRANSLATION OPERATORSarXiv: Complex Variables
Rebecca Sanders (2009)
Common Hypercyclic Vectors and the Hypercyclicity CriterionIntegral Equations and Operator Theory, 65
L. Bernal-González (2009)
Common hypercyclic functions for multiples of convolution and non-convolution operators, 137
Nathan Feldman (2001)
LINEAR CHAOS ?
F. Bayart, É. Matheron (2009)
Dynamics of Linear Operators: Author index
F. Bayart (2005)
Topological and algebraic genericity of divergence and universalityStudia Mathematica, 167
Kit Chan, Rebecca Sanders (2011)
A SOT-dense Path of Chaotic Operators with Same Hypercyclic VectorsJournal of Operator Theory
(2004)
Fernando
F. Bayart (2002)
Common hypercyclic vectors for composition operatorsarXiv: Functional Analysis
E. Abakumov, J. Gordon (2001)
Common hypercyclic vectors for multiples of backward shiftJournal of Functional Analysis, 200
Kit Chan, Rebecca Sanders (2009)
TWO CRITERIA FOR A PATH OF OPERATORS TO HAVE COMMON HYPERCYCLIC VECTORS
E. Gallardo-Gutiérrez, J. Partington (2008)
Common hypercyclic vectors for families of operators, 136
É. Matheron (2011)
Subsemigroups of transitive semigroupsErgodic Theory and Dynamical Systems, 32
G. Costakis, Mart'in Sambarino (2004)
Genericity of wild holomorphic functions and common hypercyclic vectorsAdvances in Mathematics, 182
F. Bayart (2005)
Common Hypercyclic SubspacesIntegral Equations and Operator Theory, 53
G. Costakis, Panagiotis Mavroudis (2008)
Common hypercyclic entire functions for multiples of differential operatorsColloquium Mathematicum, 111
F. Bayart, S. Grivaux (2006)
Frequently hypercyclic operatorsTransactions of the American Mathematical Society, 358
F. Bayart (2011)
Dynamics of holomorphic groupsSemigroup Forum, 82
S. Shkarin (2008)
Universal elements for non-linear operators and their applicationsJournal of Mathematical Analysis and Applications, 348
F. Bayart, G. Costakis, D. Hadjiloucas (2009)
Topologically transitive skew-products of operatorsErgodic Theory and Dynamical Systems, 30
K. Grosse-Erdmann (1999)
UNIVERSAL FAMILIES AND HYPERCYCLIC OPERATORSBulletin of the American Mathematical Society, 36
F. León-Saavedra, V. Müller (2004)
Rotations of Hypercyclic and Supercyclic OperatorsIntegral Equations and Operator Theory, 50
(1929)
Démonstration d’ un théorèm élèmentaire sur les fonctions entières
S. Shkarin (2012)
Remarks on common hypercyclic vectorsJournal of Functional Analysis, 258
K. Grosse-Erdmann (1987)
Holomorphe Monster und universelle Funktionen
Kit Chan, Rebecca Sanders (2008)
Common supercyclic vectors for a path of operatorsJournal of Mathematical Analysis and Applications, 337
G. Costakis (2010)
Common Cesàro hypercyclic vectorsStudia Mathematica, 201
F. Bayart, É. Matheron (2009)
Dynamics of Linear Operators
(2007)
Approximation by translates of entire functions, Complex and harmonic analysis
A Conejero, V Müller, A Peris (2007)
Hypercyclic behaviour of operators in a hypercyclic $$C_0$$ C 0 -semigroupJ. Funct. Anal., 244
Kit Chan, Rebecca Sanders (2012)
Common hypercyclic vectors for the unitary orbit of a hypercyclic operatorJournal of Mathematical Analysis and Applications, 387
Let $${\mathcal {H}}({\mathbb {C}})$$ H ( C ) be the set of entire functions endowed with the topology of local uniform convergence. Fix a sequence of non-zero complex numbers $$({\lambda }_n)$$ ( λ n ) with $$\liminf _{n}\frac{|{\lambda }_{n+1}|}{|{\lambda }_n|}>2.$$ lim inf n | λ n + 1 | | λ n | > 2 . We prove that there exists no entire function $$f$$ f such that for every $$b\in \mathbb {C}\setminus \{ 0\}$$ b ∈ C \ { 0 } the set $$\{ f(z+{\lambda }_nb): n=1,2,\ldots \}$$ { f ( z + λ n b ) : n = 1 , 2 , … } is dense in $${\mathcal {H}}({\mathbb {C}}).$$ H ( C ) . This, on one hand gives a negative answer to Costakis (Approximation by translates of entire functions, Complex and harmonic analysis. Destech Publ., Inc., Lancaster, pp 213–219 2007, Question 2) and on the other hand shows that certain results from Tsirivas (Existence of common hypercyclic vectors for translation operators, 2014; Common hypercyclic functions for translation operators with large gaps, 2014) are sharp.
Computational Methods and Function Theory – Springer Journals
Published: Jan 29, 2015
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