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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

1 Issue per year


IMPACT FACTOR 2015: 0.512

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Open Access
Online
ISSN
2391-5455
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Volume 13, Issue 1 (Nov 2014)

Issues

Dynamics of differentiation operators on generalized weighted Bergman spaces

Liang Zhang
  • Department of Mathematics, Tianjin University, Tianjin 300072, P.R. China
/ Ze-Hua Zhou
  • Department of Mathematics, Tianjin University, Tianjin 300072, P.R. China
  • Center for Applied Mathematics, Tianjin University, Tianjin 300072, P.R. China
  • Email:
Published Online: 2014-11-20 | DOI: https://doi.org/10.1515/math-2015-0013

Abstract

The chaos of the differentiation operator on generalized weighted Bergman spaces of entire functions has been characterized recently by Bonet and Bonilla in [CAOT 2013], when the differentiation operator is continuous. Motivated by those, we investigate conditions to ensure that finite many powers of differentiation operators are disjoint hypercyclic on generalized weighted Bergman spaces of entire functions.

Keywords : Disjoint hypercyclic; Differentiation operator; Generalized weighted Bergman spaces

References

  • [1] Bernal-González L., Disjoint hypercyclic operators, Studia Math., 2007, 182(2), 113-131.

  • [2] Bonet J., Dynamics of differentiation operator on weighted spaces of entire functions, Math. Z., 2009, 261, 649-657. [Web of Science]

  • [3] Bonet J., Bonilla A., Chaos of the differentiation operator on weighted Banach spaces of entire functions, Complex Anal. Oper. Theory, 2013, 7, 33-42. [Web of Science]

  • [4] Bermúdez T., Bonilla A., Conejero J. A., Peris A., Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces, Studia Math., 2005, 170, 57-75.

  • [5] Bonilla A., Grosse-Erdmann K. G., Frequently hypercyclic operators and vectors, Ergodic Theory Dynam. Systems, 2007, 27, 383-404. Erratum: Ergodic Theory Dynam. Systems, 2009, 29, 1993-1994.

  • [6] Bayart F., Matheron É., Dynamics of linear operators, Cambridge Tracts in Mathematics, 179, Camberidge University Press, Cambridge, 2009.

  • [7] Bès J., Martin Ö., Peris A., Disjoint hypercyclic linear fractional composition operators, J. Math. Appl., 2011, 381, 843-856.

  • [8] Bès J., Martin Ö., Peris A., Shkarin S., Disjoint mixing operators, J. Funct. Anal., 2012, 263, 1283-1322.

  • [9] Bès J., Martin Ö., Sanders R., Weighted shifts and disjoint hypercyclicity, 2012, manuscript. [Web of Science]

  • [10] Bès J., Peris A., Disjointness in hypercyclicity, J. Math. Anal. Appl., 2007, 336, 297-315.

  • [11] Costakis G., Sambarino M., Topologically mixing hypercyclic operators, Proc. Amer. Math. Soc., 2004, 132(2), 385-389.

  • [12] Chen R. Y., Zhou Z. H., Hypercyclicity of weighted composition operators on the unit ball of CN, J. Korean Math. Soc., 2011, 48(5), 969-984.

  • [13] Grosse-Erdmann K. G., Peris Manguillot A., Linear Chaos, Springer, New York, 2011.

  • [14] Harutyunyan A., Lusky W., On the boundedness of the differentiation operator between weighted spaces of holomorphic functions, Studia Math., 2008, 184, 233-247.

  • [15] Lusky W., On generalized Bergman space, Studia Math., 1996, 119, 77-95.

  • [16] Lusky W., On the Fourier series of unbounded harmonic functions, J. London. Math. Soc., 2000, 61, 568-580.

  • [17] Salas H. N., Dual disjoint hypercyclic operators, J. Math. Anal. Appl., 2011, 374, 106-117.

  • [18] Shkarin S., A short proof of existence of disjoint hypercyclic operators, J. Math. Anal. Appl., 2010, 367, 713-715.

About the article

Received: 2013-06-15

Accepted: 2014-06-30

Published Online: 2014-11-20


Citation Information: Open Mathematics, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0013. Export Citation

© 2015 Liang Zhang and Ze-Hua Zhou,. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

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