Geodesic
Functions Universal for all Translation Operators in Several Complex Variables
Canadian mathematical bulletin, Tome 60 (2017) no. 3, pp. 462-469

Voir la notice de l'article provenant de la source Cambridge University Press

We prove the existence of a (in fact many) holomorphic function $f$ in ${{\mathbb{C}}^{d}}$ such that, for any $a\ne 0$ , its translations $f(\cdot +na)$ are dense in $H({{\mathbb{C}}^{d}})$ .
DOI : 10.4153/CMB-2016-069-4
Mots-clés : 47A16, 32E20, hypercyclic operator, translation operator 
Bayart, Frédéric; Gauthier, Paul M. Functions Universal for all Translation Operators in Several Complex Variables. Canadian mathematical bulletin, Tome 60 (2017) no. 3, pp. 462-469. doi: 10.4153/CMB-2016-069-4
@article{10_4153_CMB_2016_069_4,
     author = {Bayart, Fr\'ed\'eric and Gauthier, Paul M},
     title = {Functions {Universal} for all {Translation} {Operators} in {Several} {Complex} {Variables}},
     journal = {Canadian mathematical bulletin},
     pages = {462--469},
     year = {2017},
     volume = {60},
     number = {3},
     doi = {10.4153/CMB-2016-069-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-069-4/}
}
TY  - JOUR
AU  - Bayart, Frédéric
AU  - Gauthier, Paul M
TI  - Functions Universal for all Translation Operators in Several Complex Variables
JO  - Canadian mathematical bulletin
PY  - 2017
SP  - 462
EP  - 469
VL  - 60
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-069-4/
DO  - 10.4153/CMB-2016-069-4
ID  - 10_4153_CMB_2016_069_4
ER  - 
%0 Journal Article
%A Bayart, Frédéric
%A Gauthier, Paul M
%T Functions Universal for all Translation Operators in Several Complex Variables
%J Canadian mathematical bulletin
%D 2017
%P 462-469
%V 60
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-069-4/
%R 10.4153/CMB-2016-069-4
%F 10_4153_CMB_2016_069_4

[1] [1] Bayart, E, Common hypercyclic vectors for high dimensional families of operators. Int. Math. Res. Not. IMRN 2016, no. 21, 6512–6552. http://dx.doi.Org/10.1093/imrn/rnv354 Google Scholar

[2] [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 Google Scholar

[3] [3] Birkhoff, G. D., Demonstration d'un theoreme elementaire sur les fonctions entieres. C. R. Acad. Sci. Paris 189(1929), 473–475. Google Scholar

[4] [4] Costakis, G. and Sambarino, M., Genericity of wild holomorphic functions and common hypercyclic vectors. Adv. Math. 182(2004), 278–306. http://dx.doi.Org/10.1016/S0001-8708(03)00079-3 Google Scholar

[5] [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 Google Scholar

[6] [6] Stout, E. L., Polynomial convexity. Progress in Mathematics, 261, Birkhauser Boston, Inc., Boston, MA, 2007. Google Scholar

[7] [7] Tsirivas, N., Common hypercyclic functions for translation operators with large gaps. J. Funct. Anal. 272(2017), 2726–2751. http://dx.doi.Org/10.1016/j.jfa.2O16.11.010 Google Scholar

[8] [8] Tsirivas, N., Common hypercyclic functions for translation operators with large gaps. II. arxiv:1412.1963 Google Scholar

[9] [9] Tsirivas, N., Existence of common hypercyclic vectors for translation operators. arxiv:1411.7815 Google Scholar

Cité par Sources :