Comptes Rendus
no. 3
Functional analysis/Complex analysis
Dynamics of weighted composition operators in the unit ball
[Dynamiques des opérateurs de composition pondérés dans la boule unité]

Présenté par : the Editorial Board

Zhong-Shan Fang1 ; Ze-Hua Zhou2
1 Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, PR China
2 School of Mathematics, Tianjin University, Tianjin 300354, PR China
Comptes Rendus. Mathématique, Volume 357 (2019) no. 3, pp. 278-283.

Nous étudions dans cette Note le comportement dynamique des opérateurs de composition pondérés agissant sur l'espace des fonctions holomorphes sur la boule unité de CN.

In the present paper, we investigate the dynamic behavior of weighted composition operators acting on the space of holomorphic functions on the unit ball in CN.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2019.02.003
Zhong-Shan Fang 1 ; Ze-Hua Zhou 2

1 Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, PR China
2 School of Mathematics, Tianjin University, Tianjin 300354, PR China 
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Zhong-Shan Fang; Ze-Hua Zhou. Dynamics of weighted composition operators in the unit ball. Comptes Rendus. Mathématique, Volume 357 (2019) no. 3, pp. 278-283. doi : 10.1016/j.crma.2019.02.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.02.003/

[1] F. Bayart A class of linear fractional maps of the ball and its composition operators, Adv. Math., Volume 209 (2007), pp. 649-665

[2] J. Bès Dynamics of weighted composition operators, Complex Anal. Oper. Theory, Volume 8 (2014) no. 1, pp. 159-176

[3] C.C. Cowen; B.D. MacCluer Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, FL, USA, 1995

[4] N.S. Feldman n-Weakly hypercyclic and n-weakly supercyclic operators, J. Funct. Anal., Volume 263 (2012), pp. 2255-2299

[5] L. Hörmander An Introduction to Complex Analysis in Several Variables, North-Holland, Amsterdam, 1990

[6] J.H. Shapiro Composition Operators and Classical Function Theory, Springer-Verlag, New York, 1993

[7] B. Yousefi; H. Rezaei Hypercyclic property of weighted composition operators, Proc. Amer. Math. Soc., Volume 135 (2007) no. 10, pp. 3263-3271

[8] S. Zajac Hypercyclicity of composition operators in Stein manifolds, Proc. Amer. Math. Soc., Volume 144 (2016) no. 9, pp. 3991-4000

Cité par Sources :

☆ The work was supported in part by the National Natural Science Foundation of China (Grant No. 11771323), and also supported in part by the Science and Technology Development Fund of Tianjin Commission for Higher Education (Grant No. 2017KJ095).

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