대한수학회지 (Journal of the Korean Mathematical Society)

  • 제48권5호
  • /
  • Pages.969-984
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  • 2011
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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HYPERCYCLICITY OF WEIGHTED COMPOSITION OPERATORS ON THE UNIT BALL OF ℂN

  • Chen, Ren-Yu (Department of Mathematics Tianjin University) ;
  • Zhou, Ze-Hua (Department of Mathematics Tianjin University)
  • 투고 : 2010.02.26
  • 발행 : 2011.09.01
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초록

This paper discusses the hypercyclicity of weighted composition operators acting on the space of holomorphic functions on the open unit ball $B_N$ of $\mathbb{C}^N$. Several analytic properties of linear fractional self-maps of $B_N$ 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.

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참고문헌

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피인용 문헌

  1. Hypercyclicity of weighted composition operators on a weighted Dirichlet space vol.59, pp.7, 2014, https://doi.org/10.1080/17476933.2013.809573
  2. Disjoint mixing linear fractional composition operators in the unit ball vol.353, pp.10, 2015, https://doi.org/10.1016/j.crma.2015.07.005
  3. HEREDITARILY HYPERCYCLICITY AND SUPERCYCLICITY OF WEIGHTED SHIFTS vol.51, pp.2, 2014, https://doi.org/10.4134/JKMS.2014.51.2.363
  4. Disjoint mixing composition operators on the Hardy space in the unit ball vol.352, pp.4, 2014, https://doi.org/10.1016/j.crma.2014.01.017
  5. Dynamics of composition operators on weighted Bergman spaces vol.27, pp.1, 2016, https://doi.org/10.1016/j.indag.2015.11.012