Annals of Functional Analysis

Functional equations on double coset hypergroups

Żywilla Fechner and László Székelyhidi

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Abstract

In this paper we describe the complex-valued solutions defined on a double coset hypergroup of the exponential, additive, and quadratic functional equations. Moreover, the m-sine functions on a double coset hypergroup are discussed. The double coset hypergroup we consider is closely related to affine groups and spherical functions on them.

Article information

Source
Ann. Funct. Anal., Volume 8, Number 3 (2017), 411-423.

Dates
Received: 10 August 2016
Accepted: 15 November 2016
First available in Project Euclid: 13 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.afa/1494640815

Digital Object Identifier
doi:10.1215/20088752-2017-0006

Mathematical Reviews number (MathSciNet)
MR3690003

Zentralblatt MATH identifier
1369.43003

Subjects
Primary: 43A62: Hypergroups
Secondary: 39B99: None of the above, but in this section 20N20: Hypergroups

Keywords
hypergroup functional equation affine group

Citation

Fechner, Żywilla; Székelyhidi, László. Functional equations on double coset hypergroups. Ann. Funct. Anal. 8 (2017), no. 3, 411--423. doi:10.1215/20088752-2017-0006. https://projecteuclid.org/euclid.afa/1494640815


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References

  • [1] R. Artzy, Linear Geometry, Addison-Wesley, Reading, MA, 1966.
  • [2] W. R. Bloom and H. Heyer, Harmonic Analysis of Probability Measures on Hypergroups, De Gruyter Stud. Math. 20, de Gruyter, Berlin, 1995.
  • [3] J. Dieudonné, Treatise on Analysis, VI, Pure Appl. Math. 10-VI, Academic Press, New York, 1978.
  • [4] Ż. Fechner and L. Székelyhidi, Sine functions on hypergroups, Arch. Math. (Basel) 106 (2016), no. 4, 371–382.
  • [5] P. Hermann, Representations of double coset hypergroups and induced representations, Manuscripta Math. 88 (1995), no. 1, 1–24.
  • [6] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, I, Springer, Berlin, 1979.
  • [7] R. C. Lyndon, Groups and Geometry, London Math. Soc. Lecture Note Ser. 101, Cambridge Univ. Press, Cambridge, 1985.
  • [8] L. Székelyhidi, Functional Equations on Hypergroups, World Scientific, Hackensack, NJ, 2013.