DOI QR코드

DOI QR Code

CHAOTIC PROPERTY OF WEIGHTED COMPOSITION OPERATORS

  • Rezaei, Hamid (Department of Mathematics College of Sciences Yasouj University)
  • Received : 2009.04.13
  • Published : 2011.11.30

Abstract

In the present paper, we study the chaotic property of weighted composition operators acting on the holomorphic function space $H(\mathbb{U})$.

Keywords

References

  1. G. D. Birkhoff, Demonstration d'un theoreme elementaire sur les fonctions entieres, C. R. Acad. Sci. Paris 189 (1929), 473-475.
  2. P. S. Bourdon and J. H. Shapiro, Cyclic phenomena for composition operators, Mem. Amer. Math. Soc. 125 (1997), no. 596, x+105 pp.
  3. 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. https://doi.org/10.1512/iumj.1991.40.40064
  4. 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. https://doi.org/10.1090/S0002-9947-1981-0607108-9
  5. P. L. Duren, Theory of $H^p$ Spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York, 1970; reprinted by Dover, 2000.
  6. 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. https://doi.org/10.1090/S0002-9939-1987-0884467-4
  7. G. Godefroy and J. H. Shapiro, Operators with dense invariant cyclic vector manifolds, J. Funct. Anal. 98 (1991), no. 2, 229-269. https://doi.org/10.1016/0022-1236(91)90078-J
  8. K.-G. Grosse-Erdmann, Hypercyclic and chaotic weighted shifts, Studia Math. 139 (2000), no. 1, 47-68. https://doi.org/10.4064/sm-139-1-47-68
  9. G. R. MacLane, Sequences of derivatives and normal families, J. Analyse Math. 2 (1952), 72-87. https://doi.org/10.1007/BF02786968
  10. H. N. Salas, Hypercyclic weighted shifts, Trans. Amer. Math. Soc. 347 (1995), no. 3, 993-1004. https://doi.org/10.2307/2154883
  11. J. H. Shapiro, Composition Operators and Classical Function Theory, Springer-Verlag, New York, 1993.
  12. J. H. Shapiro, Notes on dynamics of linear operator, http://www.math.msu.edu/shapiro, (2001).
  13. B. Yousefi and H. Rezaei, Hypercyclic property of weighted composition operators, Proc. Amer. Math. Soc. 135 (2007), no. 10, 3263-3271. https://doi.org/10.1090/S0002-9939-07-08833-8

Cited by

  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. Dynamics of Weighted Composition Operators vol.8, pp.1, 2014, https://doi.org/10.1007/s11785-012-0281-3