Skip to main content
SpringerLink
Log in

Almost Automorphic Distributions

  • Published:
Mediterranean Journal of Mathematics Aims and scope Submit manuscript

Abstract

The paper deals with the concept of almost automorphy in the setting of Sobolev–Schwartz distributions. The definition, the characterizations and the main properties of these distributions are studied. We also tackle the existence of distributional almost automorphic solutions of linear difference differential equations.

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. Bochner, S.: Uniform convergence of monotone sequences of functions. Proc. Natl. Acad. Sci. USA 47, 582–585 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bochner, S.: A new approch to almost periodicity. Proc. Natl. Acad. Sci. USA 48, 2039–2043 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bochner, S.: Continuous mappings of almost automorphic functions and almost periodic functions. Proc. Natl. Acad. Sci. USA 52, 907–910 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  4. Casarino, V.: Characterization of almost automorphic groups and semigroups. Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. 5, 219–235 (2000)

  5. Hale, J.K., Verduyn Lunel, S.M.: Introduction to Functional Differential Equations. Springer, Berlin (1993)

    Book  MATH  Google Scholar 

  6. Schwartz, L.: Théorie des distributions, 2nd edn. Hermann, Paris (1966)

    MATH  Google Scholar 

  7. Sobolev, S.L.: Applications of Functional Analysis in Mathematical Physics. Translations of Mathematical Monographs. vol. 7, American Mathematical Society (1963)

  8. Veech, W.A.: Almost automorphic functions on groups. Am. J. Math. 87, 719–751 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  9. Zaidman, S.: Existence of asymptotically almost periodic and almost automorphic solutions for some classes of abstract differential equations. Ann. Sc. Math. Québec 13, 79–88 (1989)

    MathSciNet  MATH  Google Scholar 

  10. Zaki, M.: Almost automorphic solutions of certain abstract differential equations. Annali. di Mat. Pura ed Appl. Ser. 4. 101 , 91–114 (1974)

Download references

Author information

Authors and Affiliations

  1. Laboratory of Mathematical Analysis and Applications, University of Oran 1 Ahmed Ben Bella, 31000, Oran, Algeria

    Chikh Bouzar & Fatima Zohra Tchouar

Authors
  1. Chikh Bouzar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fatima Zohra Tchouar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chikh Bouzar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bouzar, C., Tchouar, F.Z. Almost Automorphic Distributions. Mediterr. J. Math. 14, 151 (2017). https://doi.org/10.1007/s00009-017-0953-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00009-017-0953-3

Mathematics Subject Classification

Keywords

Search

Navigation