International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

On Estimates for the Dunkl Transform in the Space L2,α(R)

  • Mohamed El Hamma*
  • Radouan Daher

    * Corresponding author

    Abstract

    In this paper, we study two estimates useful in applications are proved for the Dunkl transform in a Hilbert space L2,α(R) = L2(R,|x|2α+1dx), α >-1/2 as applied to some classes of functions characterized by a generalized modulus of continuity.

    How to Cite

    M. El Hamma, R. Daher, On Estimates for the Dunkl Transform in the Space L2,α(R), Int. J. Anal. Appl. 6 (2014), 53–62.

    BibTeX
    @article{Hamma2014,
  author  = {El Hamma, Mohamed and Daher, Radouan},
  title   = {On Estimates for the Dunkl Transform in the Space L2,α(R)},
  journal = {Int. J. Anal. Appl.},
  volume  = {6},
  year    = {2014},
  pages   = {53--62},
  doi     = {}
}

    References

    • [1] V. A. Abilov and F. V. Abilova, Approximation of Functions by Fourier-Bessel Sums, Izv. Vyssh. Uchebn. Zaved. Mat., 8(2001), 3-9 .
    • [2] V. A. Abilov, F. V. Abilova, and M.K. Kerimov Some Remarks Concerning the Fourier Transform in the Space L2(R), Zh. Vychisl. Mat. Mat. Fiz., 48 (2008), 2113-2120.
    • [3] H. Bateman and A.Erd ´elyi, Higher Transcendental Functions, Vol II(Mc Graw-Hill, New York, 1953; Nauka, Moscow, 1971).
    • [4] E.S. Belkina and S.S. Platonov, Equivalence of K-Functionnals and Modulus of Smoothness Constructed by Generalized Dunkl Translations, Izv. Vyssh. Uchebn. Zaved. Mat., 8 (2008), 3-15.
    • [5] C.F. Dunkl, Differential-difference operators associated to reflexion groups, Trans. Amer. Math. Soc., 311(1989), 167-183.
    • [6] C.F. Dunkl, Hankel transforms associated to finite reflection groups inProceedings of Special Session on Hypergeometric Functions on Domains of Positivity, Jack Polynomials and Applications, Proceedings, Tampa 1991, Contemp. Math. 138(1992) 123-138.
    • [7] M.F.E. Jeu, The Dunkl transform , Inv. Math. 113 (1993) 147-162.
    • [8] M.R ¨osler, Bessel-type signed hypergroup on R in: H.Heyer, A.Mukherjea (Eds.)Probability Measure on Groups and Related Structures, (Proc. Conf. Oberwolfach, 1994), World Scientific, Singapore, 1995, 292-304.
    • [9] N.B. Salem and S. Kallel, Mean-Periodic Function Associated with the Dunkl operators, Adv. Integral Transforms Spec. Funct. 15(2)(2004), 155-179.