- -

Chaos of the Differentiation Operator on Weighted Banach Spaces of Entire Functions

RiuNet: Institutional repository of the Polithecnic University of Valencia

Share/Send to

Cited by

Statistics

Chaos of the Differentiation Operator on Weighted Banach Spaces of Entire Functions

Show full item record

Bonet Solves, JA.; Bonilla, A. (2013). Chaos of the Differentiation Operator on Weighted Banach Spaces of Entire Functions. Complex Analysis and Operator Theory. 7(1):33-42. doi:10.1007/s11785-011-0134-5

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/40457

Files in this item

Item Metadata

Title: Chaos of the Differentiation Operator on Weighted Banach Spaces of Entire Functions
Author: Bonet Solves, José Antonio Bonilla, Antonio
UPV Unit: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Issued date:
Abstract:
Motivated by recent work on the rate of growth of frequently hypercyclic entire functions due to Blasco, Grosse-Erdmann and Bonilla, we investigate conditions to ensure that the differentiation operator is chaotic or ...[+]
Subjects: Chaotic operator , Differentiation operator , Frequently hypercyclic operator , Hypercyclic operator , Weighted spaces of entire functions
Copyrigths: Reserva de todos los derechos
Source:
Complex Analysis and Operator Theory. (issn: 1661-8254 )
DOI: 10.1007/s11785-011-0134-5
Publisher:
Springer Verlag (Germany)
Publisher version: http://dx.doi.org/10.1007/s11785-011-0134-5
Project ID:
MICINN and FEDER [Project MTM 2007-62643]
MICINN and FEDER [Project MTM 2010-15200]
GV [Project Prometeo/2008/101]
UPV [Project 2773]
MICINN and FEDER [Project MTM2008-05891]
Thanks:
J. Bonet is partially supported by MICINN and FEDER Projects MTM 2007-62643 and MTM2010-15200, GV Project Prometeo/2008/101 and UPV Project 2773. A. Bonilla is supported by MICINN and FEDER Project MTM2008-05891.
Type: Artículo

References

Bayart F., Grivaux S.: Hypercyclicité: le rôle du spectre ponctuel unimodulaire. C. R. Math. Acad. Sci. Paris 338, 703–708 (2004)

Bayart F., Grivaux S.: Frequently hypercyclic operators. Trans. Am. Math. Soc. 358, 5083–5117 (2006)

Bayart F., Matheron E.: Dynamics of Linear Operators, Cambridge Tracts in Mathematics, Vol. 179. Cambridge University Press, Cambridge (2009) [+]
Bayart F., Grivaux S.: Hypercyclicité: le rôle du spectre ponctuel unimodulaire. C. R. Math. Acad. Sci. Paris 338, 703–708 (2004)

Bayart F., Grivaux S.: Frequently hypercyclic operators. Trans. Am. Math. Soc. 358, 5083–5117 (2006)

Bayart F., Matheron E.: Dynamics of Linear Operators, Cambridge Tracts in Mathematics, Vol. 179. Cambridge University Press, Cambridge (2009)

Bernal-Gonz alez L., Bonilla A.: Exponential type of hypercyclic entire functions. Arch. Math. (Basel) 78, 283–290 (2002)

Bierstedt K.D., Bonet J., Galbis A.: Weighted spaces of holomorphic functions on balanced domains. Mich. Math. J. 40, 271–297 (1993)

Blasco O., Bonilla A., Grosse-Erdmann K.-G.: Rate of growth of frequently hypercyclic functions. Proc. Edinburgh Math. Soc. 53, 39–59 (2010)

Bonilla A., Grosse-Erdmann K.-G.: On a theorem of Godefroy and Shapiro. Integr. Equa. Oper. Theory 56, 151–162 (2006)

Bonilla, A., Grosse-Erdmann, K.-G.: Frequently hypercyclic operators and vectors, Ergodic Theory Dynam. Systems 27 (2007), 383–404. Erratum: Ergodic Theory Dynam. Systems 29 (6)(2009), 1993–1994

Bonet J.: Dynamics of the differentiation operator on weighted spaces of entire functions. Math. Z. 261, 649–657 (2009)

Grivaux, S.: A new class of frequently hypercyclic operators, with applications. to appear in Indiana Univ. Math. J.

Grosse-Erdmann K.-G.: On the universal functions of G. R. MacLane. Complex Variables Theory Appl. 15, 193–196 (1990)

Grosse-Erdmann K.-G.: Universal families and hypercyclic operators. Bull. Am. Math. Soc. (N.S.) 36, 345–381 (1999)

Grosse-Erdmann K.-G.: Rate of growth of hypercyclic entire functions. Indag. Math. (N.S.) 11, 561–571 (2000)

Grosse-Erdmann K.G.: Recent developments in hypercyclicity. Rev. R. Acad. Cien. Serie A Mat. 97, 273–286 (2003)

Grosse-Erdmann K.G.: A weak criterion for vector-valued holomorphy. Math. Proc. Cambridge Philos. Soc. 136, 399–411 (2004)

Grosse-Erdmann, K.G., Peris, A.: Linear Chaos. Springer, Berlin (to appear)

Harutyunyan A., Lusky W.: On the boundedness of the differentiation operator between weighted spaces of holomorphic functions. Stud. Math. 184, 233–247 (2008)

Lusky W.: On generalized Bergman spaces. Stud. Math. 119, 77–95 (1996)

Lusky W.: On the Fourier series of unbounded harmonic functions. J. Lond. Math. 61, 568–580 (2000)

Lusky W.: On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Stud. Math. 175, 19–45 (2006)

MacLane G.R.: Sequences of derivatives and normal families. J. Anal. Math. 2, 72–87 (1952/53)

Murray J.D.: Asymptotic Analysis. Springer, New York (1984)

Shkarin S.A.: On the growth of D-universal functions. Univ. Math. Bull. 48(6), 49–51 (1993)

[-]

This item appears in the following Collection(s)

Show full item record