Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지
DOI QR코드

DOI QR Code

ABSOLUTE CONTINUITY OF THE REPRESENTING MEASURES OF THE HYPERGEOMETRIC TRANSLATION OPERATORS ATTACHED TO THE ROOT SYSTEM OF TYPE B2 AND C2

  • Trimeche, Khalifa (Department of Mathemtaics Faculty of sciences of Tunis University Tunis El-Manar)
  • Received : 2014.06.09
  • Accepted : 2014.12.10
  • Published : 2014.12.30
Download PDF
⟨ Previous Next ⟩

Abstract

We prove in this paper the absolute continuity of the representing measures of the hypergeometric translation operators $\mathcal{T}_x$ and $\mathcal{T}_x^W$ associated respectively to the Cherednik operators and the Heckman-Opdam theory attached to the root system of type $B_2$ and $C_2$ which are studied in [9].

Keywords

References

  1. N. Bourbaki, Elements de Mathematiques Fascule XXI. Integration des mesures, Chapitre 5, Hermann, Paris, 1967.
  2. I. Cherednik, A unification of Knizhnik-Zamolodchnikov equations and Dunkl operators via affne Hecke algebras, Invent. Math. 106 (1991), 411-432. https://doi.org/10.1007/BF01243918
  3. G.H.Heckman and E.M.Opdam, Root systems and hypergeometric functions. I, Compositio. Math. 64 (1987), 329-352.
  4. G.J.Heckman and H. Schlichtkrull, Harmonic analysis and special functions on symmetric spaces, Academic Press 1994.
  5. E.M.Opdam, Harmonic analysis for certain representations of graded Hecke algebras, Acta Math. 175 (1995), 75-121. https://doi.org/10.1007/BF02392487
  6. W. Rudin. Real and complex analysis, Mc Graw Hill Inc. second edition. 1974.
  7. B.Schapira, Contributions to the hypergeometric function theroy of Heckman and Opdam : sharp estimates, Schwartz space, heat kernel, Geom. Funct. Anal. 18 (2008), 222-250. https://doi.org/10.1007/s00039-008-0658-7
  8. K. Trimeche, Harmonic analysis associated with the Cherednik operators and the Heckman-Opdam theory, Adv. Pure Appl. Math. 2 (2011), 23-46.
  9. K. Trimeche, The positivity of the hypergeometric translation operators associated to the Cherednik operators and the Heckman-Opdam theory attached to the root system of type $B_2$ and $C_2$, Korean J. Math. 22 (1) (2014), 1-28. https://doi.org/10.11568/kjm.2014.22.1.1

Cited by

  1. GENERALIZED WAVELETS AND THE GENERALIZED WAVELET TRANSFORM ON ℝd FOR THE HECKMAN-OPDAM THEORY vol.24, pp.2, 2016, https://doi.org/10.11568/kjm.2016.24.2.235