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http://dx.doi.org/10.4134/BKMS.2011.48.6.1119

CHAOTIC PROPERTY OF WEIGHTED COMPOSITION OPERATORS  

Rezaei, Hamid (Department of Mathematics College of Sciences Yasouj University)
Publication Information
Bulletin of the Korean Mathematical Society / v.48, no.6, 2011 , pp. 1119-1124 More about this Journal
Abstract
In the present paper, we study the chaotic property of weighted composition operators acting on the holomorphic function space $H(\mathbb{U})$.
Keywords
weighted composition operator; hypercyclic operator; Denjoy-Wolff point; Julia-Caratheodory theorem; linear-fractional model theorem; chaotic operator;
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1 C. C. Cowen, Iteration and the solution of functional equations for functions analytic In the unit disk, Trans. Amer. Math. Soc. 265 (1981), no. 1, 69-95.   DOI   ScienceOn
2 P. L. Duren, Theory of $H^p$ Spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York, 1970; reprinted by Dover, 2000.
3 R. M. Gethner and J. H. Shapiro, Universal vectors for operators on spaces of holomorphic functions, Proc. Amer. Math. Soc. 100 (1987), no. 2, 281-288.   DOI   ScienceOn
4 G. Godefroy and J. H. Shapiro, Operators with dense invariant cyclic vector manifolds, J. Funct. Anal. 98 (1991), no. 2, 229-269.   DOI
5 K.-G. Grosse-Erdmann, Hypercyclic and chaotic weighted shifts, Studia Math. 139 (2000), no. 1, 47-68.   DOI
6 G. R. MacLane, Sequences of derivatives and normal families, J. Analyse Math. 2 (1952), 72-87.   DOI
7 H. N. Salas, Hypercyclic weighted shifts, Trans. Amer. Math. Soc. 347 (1995), no. 3, 993-1004.   DOI   ScienceOn
8 J. H. Shapiro, Composition Operators and Classical Function Theory, Springer-Verlag, New York, 1993.
9 J. H. Shapiro, Notes on dynamics of linear operator, http://www.math.msu.edu/shapiro, (2001).
10 B. Yousefi and H. Rezaei, Hypercyclic property of weighted composition operators, Proc. Amer. Math. Soc. 135 (2007), no. 10, 3263-3271.   DOI   ScienceOn
11 K. C. Chan and J. H. Shapiro, The cyclic behavior of translation operator on Hilbert spaces of entire functions, Indiana Univ. Math. J. 40 (1991), no. 4, 1421-1449.   DOI
12 G. D. Birkhoff, Demonstration d'un theoreme elementaire sur les fonctions entieres, C. R. Acad. Sci. Paris 189 (1929), 473-475.
13 P. S. Bourdon and J. H. Shapiro, Cyclic phenomena for composition operators, Mem. Amer. Math. Soc. 125 (1997), no. 596, x+105 pp.