HYPERCYCLICITY OF WEIGHTED COMPOSITION OPERATORS ON THE UNIT BALL OF ℂN

Title & Authors
HYPERCYCLICITY OF WEIGHTED COMPOSITION OPERATORS ON THE UNIT BALL OF ℂN
Chen, Ren-Yu; Zhou, Ze-Hua;

Abstract
This paper discusses the hypercyclicity of weighted composition operators acting on the space of holomorphic functions on the open unit ball $\small{B_N}$ of $\small{\mathbb{C}^N}$. Several analytic properties of linear fractional self-maps of $\small{B_N}$ are given. According to these properties, a few necessary conditions for a weighted composition operator to be hypercyclic in the space of holomorphic functions are proved. Besides, the hypercyclicity of adjoint of weighted composition operators are studied in this paper.
Keywords
hypercyclic operator;weighted composition operator;linear fractional map;generalized Cayley transform;Heisenberg transform;Denjoy-Wollf point;
Language
English
Cited by
1.
HEREDITARILY HYPERCYCLICITY AND SUPERCYCLICITY OF WEIGHTED SHIFTS,;;

대한수학회지, 2014. vol.51. 2, pp.363-382
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Hypercyclicity of weighted composition operators on a weighted Dirichlet space, Complex Variables and Elliptic Equations, 2014, 59, 7, 1043
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Disjoint mixing linear fractional composition operators in the unit ball, Comptes Rendus Mathematique, 2015, 353, 10, 937
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Dynamics of composition operators on weighted Bergman spaces, Indagationes Mathematicae, 2016, 27, 1, 406
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HEREDITARILY HYPERCYCLICITY AND SUPERCYCLICITY OF WEIGHTED SHIFTS, Journal of the Korean Mathematical Society, 2014, 51, 2, 363
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