Titchmarsh's Theorem for the Dunkl transform in the space L2(Rd,ωk(x)dx)

• Daher, Radouan ^[1] ; El Hamma, Mohamed ^[1]
  1. [1] University of Hassan II.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 33, Nº. 1, 2014, págs. 91-100
• Idioma: inglés
• DOI: 10.4067/S0716-09172014000100007
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• Resumen

  • Using a generalized spherical mean operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the (φ, α, β, P)-Dunkl Lipschitz condition in L2(Rd, ωk(x)dx).

• Referencias bibliográficas
  • Citas [1] V. A. Abilov and F. V. Abilova, Approximation of Functions by Fourier-Bessel Sums, Izv. Vyssh. Uchebn. Zaved. Mat., No. 8, pp....
  • [2] E. S. Belkina and S.S. Platonov, Equivalence of K-Functionals and Modulus of Smoothness Constructed by Generalized Dunkl Translations,...
  • [3] C. F. Dunkl, Differential-difference operators associated to reflection group, Trans. Amer. Math. Soc. 311, pp. 167-183, (1989).
  • [4] C. F. Dunkl, Hankel transforms associated to finite reflection groups, Contemp. Math. 138, pp. 123-138, (1992).
  • [5] C. F. Dunkl, Integral kernels with reflection group invariance , Canad. J. Math. 43, pp. 1213-1227, (1991).
  • [6] M. F. E. Jeu, The Dunkl transform, Invent. Math. 113, pp. 147-162, (1993).
  • [7] M. Maslouhi, An anlog of Titchmarsh’s Theorem for the Dunkl transform, J. Integral. Trans. Spec. Funct, Vol. 21, Issue 10, pp. 771-778,...
  • [8] M. Rosler, Positivity of Dunkl’s intertwining operator, Duke Math. J. 98, pp. 445-463, (1999). [arxiv.org/abs/q-alg/9710029].
  • [9] M. Rosler, M. Voit, Markov processes with Dunkl operators, Adv. in Appl. Math. 21, pp. 575-643, (1998).
  • [10] E. S. Titchmarsh, Introduction to the Theory of Fourier Integrals, Oxford University Press, Amen House, London, E. C. 4. (1948).
  • [11] K. Trimeche, Paley-Wiener theorems for the Dunkl transform and Dunkl translation operators, Integral Transforms Spec. Funct. 13, pp....