Functional analysis/Dynamical systems
Disjoint mixing linear fractional composition operators in the unit ball
Comptes Rendus. Mathématique, Volume 353 (2015) no. 10, pp. 937-942.

In the present paper, we investigate the disjoint mixing property of finitely many linear fractional composition operators acting on the space of holomorphic functions on the unit ball in CN, and generalize parts of the results obtained by Bès, Martin and Peris in 2011.

Dans la présente note, nous étudions la propriété de mélange disjoint pour un nombre fini d'opérateurs de composition linéaires fractionnaires agissant sur l'espace des fonctions holomorphes sur la boule unité de CN, et nous généralisons une partie des résultats obtenus par Bès, Martin et Peris en 2011.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2015.07.005
Fang, Zhong-Shan 1; Zhou, Ze-Hua 2, 3

1 Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, PR China
2 Department of Mathematics, Tianjin University, Tianjin 300072, PR China
3 Center for Applied Mathematics, Tianjin University, Tianjin 300072, PR China
@article{CRMATH_2015__353_10_937_0,
     author = {Fang, Zhong-Shan and Zhou, Ze-Hua},
     title = {Disjoint mixing linear fractional composition operators in the unit ball},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {937--942},
     publisher = {Elsevier},
     volume = {353},
     number = {10},
     year = {2015},
     doi = {10.1016/j.crma.2015.07.005},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2015.07.005/}
}
TY  - JOUR
AU  - Fang, Zhong-Shan
AU  - Zhou, Ze-Hua
TI  - Disjoint mixing linear fractional composition operators in the unit ball
JO  - Comptes Rendus. Mathématique
PY  - 2015
SP  - 937
EP  - 942
VL  - 353
IS  - 10
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2015.07.005/
DO  - 10.1016/j.crma.2015.07.005
LA  - en
ID  - CRMATH_2015__353_10_937_0
ER  - 
%0 Journal Article
%A Fang, Zhong-Shan
%A Zhou, Ze-Hua
%T Disjoint mixing linear fractional composition operators in the unit ball
%J Comptes Rendus. Mathématique
%D 2015
%P 937-942
%V 353
%N 10
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2015.07.005/
%R 10.1016/j.crma.2015.07.005
%G en
%F CRMATH_2015__353_10_937_0
Fang, Zhong-Shan; Zhou, Ze-Hua. Disjoint mixing linear fractional composition operators in the unit ball. Comptes Rendus. Mathématique, Volume 353 (2015) no. 10, pp. 937-942. doi : 10.1016/j.crma.2015.07.005. http://www.numdam.org/articles/10.1016/j.crma.2015.07.005/

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

[2] Bayart, F.; Charpentier, S. Hyperbolic composition operators on the ball, Trans. Amer. Math. Soc., Volume 365 (2013), pp. 911-938

[3] Bayart, F.; Matheron, E. Dynamics of Linear Operators, Cambridge University Press, Cambridge, UK, 2009

[4] Bès, J. Dynamics of composition operators with holomorphic symbol, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., Volume 107 (2013) no. 2, pp. 437-449

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

[6] Bès, J.; Martin, Ö.; Peris, A. Disjoint hypercyclic linear fractional composition operators, J. Math. Anal. Appl., Volume 381 (2011), pp. 843-856

[7] Bourdon, P.S.; Shapiro, J.H. Cyclic phenomena for composition operators, Mem. Amer. Math. Soc., Volume 596 (1997) no. 125, pp. 1-150

[8] Chen, R.Y.; Zhou, Z.H. Hypercyclicity of weighted composition operators on the unit ball of CN, J. Korean Math. Soc., Volume 48 (2011) no. 5, pp. 969-984

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

[10] Grosse-Erdmann, K.G.; Peris Manguillot, A. Linear Chaos, Universitext, Springer-Verlag, 2011

[11] Jiang, L.; Ouyang, C. Cyclic behavior of linear fractional composition operators in the unit ball of CN, J. Math. Anal. Appl., Volume 341 (2008), pp. 601-612

[12] Ohsawa, T. Analysis of Several Complex Variables, Translations of Mathematical Monographs, Amer. Math. Soc., 2002

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

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

Cited by Sources:

The work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11371276; 11401431) and by Tianjin City High School Science and Technology Fund Planning Project (Grant No. 20141002).