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Functions Universal for all Translation Operators in Several Complex Variables

  • Frédéric Bayart (a1) and Paul M Gauthier (a2)
Abstract

We prove the existence of a (in fact many) holomorphic function ƒ in C d such that, for any a ≠ 0, its translations f ( · + na) are dense in H(C d ).

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[1] Bayart, E, Common hypercyclic vectors for high dimensional families of operators. Int. Math. Res. Not. IMRN 2016, no. 21, 65126552. http://dx.doi.Org/10.1093/imrn/rnv354
[2] Bayart, E and Matheron, E., Dynamics of linear operators. Cambridge Tracts in Mathematics, 179, Cambridge University Press, Cambridge, 2009. http://dx.doi.Org/10.1017/CBO9780511581113
[3] Birkhoff, G. D., Demonstration d'un theoreme elementaire sur les fonctions entieres. C. R. Acad. Sci. Paris 189(1929), 473475.
[4] Costakis, G. and Sambarino, M., Genericity of wild holomorphic functions and common hypercyclic vectors. Adv. Math. 182(2004), 278306. http://dx.doi.Org/10.1016/S0001-8708(03)00079-3
[5] Grosse-Erdmann, K.-G. and Peris, A., Linear chaos. Universitext, Springer, London 2011. http://dx.doi.Org/10.1007/978-1-4471-2170-1
[6] Stout, E. L., Polynomial convexity. Progress in Mathematics, 261, Birkhauser Boston, Inc., Boston, MA, 2007.
[7] Tsirivas, N., Common hypercyclic functions for translation operators with large gaps. J. Funct. Anal. 272(2017), 27262751. http://dx.doi.Org/10.1016/j.jfa.2O16.11.010
[8] Tsirivas, N., Common hypercyclic functions for translation operators with large gaps. II. arxiv:1412.1963
[9] Tsirivas, N., Existence of common hypercyclic vectors for translation operators. arxiv:1411.7815
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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