Skip to main content
SpringerLink
Log in

Commutation relations and hypercyclic operators

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

Abstract

In this paper we establish hypercyclicity of continuous linear operators on \({H(\mathbb{C})}\) that satisfy certain commutation relations.

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. Aron R., Markose D.: On universal functions. J. Korean Math. Soc. 41, 65–76 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. F. Bayart and E. Matheron Dynamics of linear operators, Cambridge University Press, 2009.

  3. Betancor J.J., Sifi M., Trimeche K.: Hypercyclic and chaotic convolution operators associated with the Dunkl operators on \({\mathbb{C}}\) , Acta Math. Hungar. 106, 101–116 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Birkhoff G. D.: Demonstration d’un theoreme elementaire sur les fonctions entieres. C.R. Acad. Sci. Paris 189, 473–475 (1929)

    Google Scholar 

  5. L. D. Faddeev and O. A. Yakubovskii Lectures on Quantum Mechanics for Mathematics Students, AMS, 2009.

  6. Fernandez G., Hallack A.A.: Remarks on a result about hypercyclic non-convolution operators. J. Math. Anal. Appl. 309, 52–55 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. R. E. Edwards Functional analysis: theory and applications, Dover Publications, 1995.

  8. GodefroyG.Shapiro J. H.: Operators with dense, invariant, cyclic vector manifolds. J. Funct. Anal. 98, 229–269 (1991)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  10. K.-G. Grosse-Erdmann and A. Peris Manguillot Linear chaos, Springer, 2011.

  11. D. I. Gurevich Counterexamples to a problem of L. Schwartz, (in Russian), Funkts. Anal. Prilozh. 9 (1975), 29–35 [English translation: Funct. Anal. Appl. 9 (1975), 116–120].

  12. V. E. Kim Hypercyclicity and chaotic character of generalized convolution operators generated by Gelfond-Leontev operators (in Russian), Mat. Zametki 85 (2009), 849–856 [English translation: Math. Notes 85 (2009), 807–813].

  13. A. S. Krivosheev and V. V. Napalkov Complex analysis and convolution operators, (in Russian), Usp. Mat. Nauk 47 (1992), 3–58 [English translation: Russ. Math. Surv. 47 (1992), 1–56].

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

    Article  MathSciNet  MATH  Google Scholar 

  15. Petersson H.: Supercyclic and hypercyclic non-convolution operators. J. Operator Theory 55, 133–151 (2006)

    MathSciNet  Google Scholar 

  16. Schwartz L.: Theorie generale des fonctions moyenne-periodique. Ann. Math. 48, 867–929 (1947)

    Article  Google Scholar 

  17. O. Vallee and M. Soares Airy functions and applications to physics, Imperial College Press, 2004.

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics with Computing Centre, Russian Academy of Sciences, 112 Chernyshevsky str., 450008, Ufa, Russia

    Vitaly E. Kim

Authors
  1. Vitaly E. Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vitaly E. Kim.

Additional information

This work is partially supported by the Russian Foundation for Basic Research (projects 11-01-00572 and 11-01-97019).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kim, V.E. Commutation relations and hypercyclic operators. Arch. Math. 99, 247–253 (2012). https://doi.org/10.1007/s00013-012-0431-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00013-012-0431-x

Mathematics Subject Classification (2010)

Keywords

Search

Navigation