Skip to main content
SpringerLink
Log in

The Hypergroup Associated with the Cherednik Operators and Applications to the Infinitely Divisible Probabilities and Convolution Semigroups

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

Abstract

In this paper we define the hypergroup \((\mathbb {R}^d, *_\mathcal {H})\) associated with the Cherednik operators on \(\mathbb {R}^d\) and we use the harmonic analysis on this hypergroup to study the infinite divisible probabilities and the convolution semigroups on the hypergroup \((\mathbb {R}^d, *_\mathcal {H})\).

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. Bloom, W.R., Heyer, H.: Harmonic Analysis of Probability Measures on Hypergroups. Walter de Gruyter, Berlin (1995)

    Book  MATH  Google Scholar 

  2. Cherednik, I.: A unification of Knizhnik-Zamslodchnikov equations and Dunkl operators via affine Hecke algebras. Invent. Math. 106, 411–432 (1990)

    Article  MATH  Google Scholar 

  3. Cherednik, I.: Inverse Harish-Chandra transform and difference operators. Int. Math. Res. Notices (IMRN) 15, 733–750 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  4. Dunkl, C.F.: The measure algebra of a locally compact hypergroup. Tran. Am. Math. Soc. 179, 331–348 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  5. Jewett, R.I.: Spaces with an abstract convolution of measures. Adv. Math. 18(1), 1–101 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  6. Opdam, E.M.: Harmonic analysis for certain representations of graded Hecke algebras. Acta Math. 175, 75–121 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  7. Spector, R.: Aperçu de la théorie des hypergroupes. In: Analyse harmonique sur les groupes de Lie (Sém. Nancy-Strasbourg, 1973–1975), Lect. Notes Math., vol. 497, pp. 643–673. Springer, Berlin (1975)

  8. Triméche, K.: Generalized Wavelets and Hypergroups. Gordon and Breach Science Publishers, OPA (overseas Publishers Association) (1997)

  9. Triméche, K.: The trigonometric Dunkl intertwining operator and its dual associated with the Cherednik operators and the Heckman-Opdam theory. Adv. Pure Appl. Math. 1, 293–323 (2010)

    MathSciNet  MATH  Google Scholar 

  10. Triméche, K.: Harmonic analysis associated with the Cherednik operators and the Heckam-Opdam theory. Adv. Pure Appl. Math. 2, 23–46 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  11. Trimèche, K.: Positivity of the transmutation operators and absolute continuity of their representing measures for a root system on \({\mathbb{R}}^d\). Int. J. Appl. Math. 28(5), 427–453 (2015)

    MathSciNet  MATH  Google Scholar 

  12. Trimèche, K.: The positivity of the hypergeometric translation operators associated to the Cherednik operators and the Heckman-Opdam theory on \(R^d\). Adv. Pure Appl. Math. 8(2), 91–108 (2017)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences of Tunis, Campus, 2092, Tunis, Tunisia

    Amina Hassini

Authors
  1. Amina Hassini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Amina Hassini.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hassini, A. The Hypergroup Associated with the Cherednik Operators and Applications to the Infinitely Divisible Probabilities and Convolution Semigroups. Mediterr. J. Math. 14, 156 (2017). https://doi.org/10.1007/s00009-017-0951-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00009-017-0951-5

Keywords

Mathematics Subject Classification

Search

Navigation