Titchmarsh's Theorem for the Dunkl transform in the space L2(Rd,ωk(x)dx)
DOI:
https://doi.org/10.4067/S0716-09172014000100007Keywords:
Dunkl operator, Dunkl transform, generalized spherical mean operator, operador de Dunkl, transformada de Dunkl, operador esférico generalizado medio.Abstract
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).References
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[2] E. S. Belkina and S.S. Platonov, Equivalence of K-Functionals and Modulus of Smoothness Constructed by Generalized Dunkl Translations, Izv. Vyssh. Uchebn. Zaved. Mat, No. 8, pp. 3-15 (2008).
[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, (2010).
[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. 17-38, (2002).
Published
2017-03-23
How to Cite
[1]
R. Daher and M. El Hamma, “Titchmarsh’s Theorem for the Dunkl transform in the space L2(Rd,ωk(x)dx)”, Proyecciones (Antofagasta, On line), vol. 33, no. 1, pp. 91-100, Mar. 2017.
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