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2015 | 13 | 1 |
Tytuł artykułu

Dynamics of differentiation operators on generalized weighted Bergman spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2013-06-15
zaakceptowano
2014-06-30
online
2014-11-20
Twórcy
autor
  • Department of Mathematics, Tianjin University, Tianjin 300072, P.R. China
autor
  • Department of Mathematics, Tianjin University, Tianjin 300072, P.R. China, zhzhou@tju.edu.cn
  • Center for Applied Mathematics, Tianjin University, Tianjin 300072, P.R. China
Bibliografia
  • ---
  • [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.[WoS]
  • [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.[WoS]
  • [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.[WoS]
  • [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 holomorphicfunctions, 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0013
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