Skip to main content
SpringerLink
Log in

Dynamics of holomorphic groups

  • Research Article
  • Published:
Semigroup Forum Aims and scope Submit manuscript

Abstract

We show that there exist hypercyclic strongly continuous holomorphic groups of operators containing non-hypercyclic operators. We also give several counterexamples for the existence of common hypercyclic vectors in the same context.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abakumov, E., Gordon, J.: Common hypercyclic vectors for multiples of backward shift. J. Funct. Anal. 200, 494–504 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bayart, F., Matheron, É.: Dynamics of Linear Operators. Cambridge Tracts in Math, vol. 179. Cambridge University Press, Cambridge (2009)

    Book  MATH  Google Scholar 

  3. Chan, K.C., Shapiro, J.: The cyclic behavior of translation operators on Hilbert spaces of entire functions. Indiana Univ. Math. J. 40, 1421–1449 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  4. Conejero, J.A., Peris, A.: Hypercyclic translation c 0-semigroups on complex sectors. Discrete Contin. Dyn. Syst., Ser. A 25, 1195–1208 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  5. Conejero, J.A., Müller, V., Peris, A.: Hypercyclic behaviour of operators in a hypercyclic C 0-semigroup. J. Funct. Anal. 244, 342–348 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  6. Costakis, G., Sambarino, M.: Genericity of wild holomorphic functions and common hypercyclic vectors. Adv. Math. 182, 278–306 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. Godefroy, G., Shapiro, J.H.: Operators with dense, invariant, cyclic vector manifolds. J. Funct. Anal. 98, 229–269 (1991). MR 92d:47029

    Article  MATH  MathSciNet  Google Scholar 

  8. Levin, B.Ya.: Lectures on Entire Functions. Translations of Mathematical Monographs, vol. 150. Am. Math. Soc., Providence (1996)

    MATH  Google Scholar 

  9. Shkarin, S.: Universal elements for non-linear operators and their applications. J. Math. Anal. Appl. 348, 193–210 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  10. Shkarin, S.: Remarks on common hypercyclic vectors. J. Funct. Anal. 258, 132–160 (2010)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Mathématiques, Clermont Université, Université Blaise Pascal, BP 10448, 63000, Clermont-Ferrand, France

    Frédéric Bayart

  2. Laboratoire de Mathématiques, CNRS, UMR 6620, 63177, Aubiere, France

    Frédéric Bayart

Authors
  1. Frédéric Bayart
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Frédéric Bayart.

Additional information

Communicated by Markus Haase.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bayart, F. Dynamics of holomorphic groups. Semigroup Forum 82, 229–241 (2011). https://doi.org/10.1007/s00233-010-9284-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00233-010-9284-4

Keywords

Search

Navigation