Abstract
In this paper, we generalize some known results for the discrete Fourier analysis to the bounded Jacobi-Dunkl case. We define Jacobi-Dunkl distributions, then we give sufficient condition for the normal convergence of the Jacobi-Dunkl series. Finally, we state a Titchmarsh type theorem.
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Chouchene, F.: Harmonic analysis associated with the Jacobi-Dunkl operator on \(\left]-\frac{\pi }{2},\frac{\pi }{2}\right[\). J. Comput. Appl. Math. 178, 75–89 (2005)
Chouchene, F., Haouala, I.: Dirichlet theorem for Jacobi-Dunkl expansions. Numer. Funct. Anal. Optim. 42(1), 109–121 (2021)
Chouchene, F., Haouala, I.: de La Vallée Poussin approximations and Jacobi-Dunkl convolution structures, Results Math. 75 (2) (2020), 21 pages
Duren, P.L.: Theory of H\(^p\) Spaces, Pure and Applied Mathematics, vol. 38. Academic Press, NY-London (1970)
El Ouadih, S., Daher, R.: Lipschitz conditions for the generalized discrete Fourier transform associated with the Jacobi operator on \([0,\pi ]\). C. R. Math. Acad. Sci. Paris 355(3), 318–324 (2017)
Platonov, S.S.: Fourier-Jacobi harmonic analysis and approximation of functions. Izv. Ross. Akad. Nauk, Ser. Mat., 78(1), 117–166 (2014)
Younis, M.S.: Fourier Transforms of Lipschitz Functions on Compact Groups, Ph.D. Thesis, McMaster University, Hamilton, Ontario, Canada (1974)
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Haouala, I. Generalized Distributions and Jacobi-Dunkl Approximations. Results Math 77, 173 (2022). https://doi.org/10.1007/s00025-022-01701-9
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DOI: https://doi.org/10.1007/s00025-022-01701-9