Skip to main content

Functional equations for exponential polynomials

Abstract

The aim of the present paper is to describe some properties of functions with finite dimensional difference spaces by means of spectral analysis and spectral synthesis. We are going to apply these results to a version of a Levi-Civita functional equation, which has been recently studied by J. M. Almira and E. Shulman.

References

  1. Almira, J.M.: Characterization of polynomials as solutions of certain functional equations. J. Math. Anal. Appl. 459(2), 1016–1028 (2017)

    MathSciNet  Article  MATH  Google Scholar 

  2. Almira, J.M.: Characterization of functions whose forward differences are exponential polynomials. Comment. Math. Univ. Carolin 58(4), 435–442 (2017)

    MathSciNet  MATH  Google Scholar 

  3. Almira, J.M., Shulman, E.: On certain generalizations of the Levi-Civita and Wilson functional equations. Aequ. Math. 91(1), 921–931 (2017)

    MathSciNet  Article  MATH  Google Scholar 

  4. Bloom, W.R.: Heyer, Herbert, Harmonic Analysis of Probability Measures on Hypergroups. De Gruyter Studies in Mathematics, vol. 20. Walter de Gruyter & Co., Berlin (1995)

    Book  Google Scholar 

  5. Djoković, D.Ž.: A representation theorem for \((X_{1}-1)(X_{2} -1)\cdots (X_{n}-1)\) and its applications. Ann. Polon. Math. 22, 189–198 (1969/1970)

  6. Shulman, E.: Decomposable functions and representations of topological semigroup. Aequ. Math. 79(1), 13–21 (2010)

    MathSciNet  Article  MATH  Google Scholar 

  7. Székelyhidi, L.: Convolution Type Functional Equations on Topological Abelian Groups. World Scientific Publishing Co., Inc, Teaneck, NJ (1991)

    Book  MATH  Google Scholar 

  8. Székelyhidi, L.: Exponential polynomials on commutative hypergroups. Arch. Math. (Basel) 101(4), 341–347 (2013)

    MathSciNet  Article  MATH  Google Scholar 

  9. Székelyhidi, L.: Characterization of exponential polynomials on commutative hypergroups. Ann. Funct. Anal. 5(2), 53–60 (2014)

    MathSciNet  Article  MATH  Google Scholar 

  10. Székelyhidi, L.: Harmonic and Spectral Analysis. World Scientific Publishing Co, Pte. Ltd., Hackensack, NJ (2014)

    Book  MATH  Google Scholar 

  11. Székelyhidi, L.: A functional equation for exponential polynomials. Aequ. Math. 89(3), 821–828 (2015). https://doi.org/10.1007/s00010-014-0276-4

    MathSciNet  Article  MATH  Google Scholar 

  12. Székelyhidi, L.: Functional equations and stability problems on hypergroups. In: Developments in Functional Equations and Related Topics, pp. 305–331 (2017)

  13. Székelyhidi, L., Vajday, L.: Spectral analysis on commutative hypergroups. Aequ. Math. 80(1–2), 223–226 (2010)

    MathSciNet  Article  MATH  Google Scholar 

  14. Székelyhidi, L., Vajday, L.: Spectral synthesis on commutative hypergroups. Ann. Univ. Sci. Budapest. Sect. Comput. 45, 111–117 (2016)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

László Székelyhidi was partly supported by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. K111651, and by BIUST, Botswana. Żywilla Fechner was supported by the National Science Centre, Poland, Grant No. DEC-2017/01/X/ST1/00916.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Żywilla Fechner.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Fechner, Ż., Székelyhidi, L. Functional equations for exponential polynomials. Aequat. Math. 93, 535–545 (2019). https://doi.org/10.1007/s00010-018-0593-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00010-018-0593-0

Mathematics Subject Classification

  • 39B99
  • 43A62
  • 20N20

Keywords

  • Exponential polynomials
  • Levi-Civita equation
  • Hypergroups