Reproducing Formulas for the Fourier-Like Multipliers Operators in q-Rubin Setting

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Ahmed Saoudi, Reproducing Formulas for the Fourier-Like Multipliers Operators in q-Rubin Setting, Int. J. Anal. Appl., 18 (3) (2020), 366-380.

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Ahmed Saoudi

Abstract

The aim of this work is to study of the q^2 -Fourier multiplier operators on R_q and we give for them Calderon's reproducing formulas and best approximation on the q^2-analogue Sobolev type space H_q using the theory of q^2-Fourier transform and reproducing kernels.

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References

  1. J.-P. Anker, Lp Fourier multipliers on Riemannian symmetric spaces of the noncompact type, Ann. Math. 132 (1990), 597-628.
  2. J. J. Betancor, O. Ciaurri, and J. L. Varona, The multiplier of the interval [-1, 1] for the Dunkl transform on the real line, J. Funct. Ana. 242 (1) (2007), 327-336.
  3. N. Bettaibi, K. Mezlini, and M. El Guenichi, On rubin's harmonic analysis and its related positive definite functions, Acta Math. Sci. 32 (5) (2012), 1851-1874.
  4. A. Fitouhi and R. H. Bettaieb, Wavelet transforms in the q 2 -analogue Fourier analysis, Math. Sci. Res. J. 12(9) (2008), 202-214.
  5. G. Gasper and M. Rahman, Basic hypergeometric series, Cambridge University Press, 2004.
  6. F. Jackson, On a q-Definite integrals, Quart. J. Pure Appl. Math. 41 (1910), 193-203.
  7. V. Kac and P. Cheung, Quantum calculus, Springer Science & Business Media, 2001.
  8. G. Kimeldorf and G. Wahba, Some results on Tchebycheffian spline functions, J. Math. Anal. Appl. 33(1) (1971), 82-95.
  9. T. H. Koornwinder and R. F. Swarttouw, On q-analogues of the Fourier and Hankel transforms, Trans. Amer. Math. Soc. 333 (1) (1992), 445-461.
  10. T. Matsuura, S. Saitoh, and D. Trong, Approximate and analytical inversion formulas in heat conduction on multidimensional spaces, J. Inverse Ill-posed Probl. 13 (5) (2005), 479-493.
  11. R. Rubin, Duhamel solutions of non-homogeneous q 2 -analogue wave equations, Proc. Amer. Math. Soc. 135 (3) (2007), 777-785.
  12. R. L. Rubin, A q 2 -Analogue Operator for q 2 -Analogue Fourier Analysis, J. Math. Anal. Appl. 212(2) (1997), 571-582.
  13. S. Saitoh, Approximate real inversion formulas of the Gaussian convolution, Appl. Anal. 83 (7) (2004), 727-733.
  14. A. Saoudi, Calder ´on's reproducing formulas for the Weinstein L2 -multiplier operators, Asian-Eur. J. Math. https://doi. org/10.1142/S1793557121500030 (2019).
  15. A. Saoudi and A. Fitouhi, On q2 -analogue Sobolev type spaces, Le Mat. 70 (2) (2015), 63-77.
  16. A. Saoudi and A. Fitouhi, Three Applications In q 2 -Analogue Sobolev Spaces, Appl. Math. E-Notes. 17 (2017), 1-9.
  17. A. Saoudi and A. Fitouhi, Littlewood-Paley decomposition in quantum calculus, Appl. Anal. https://doi.org/10.1080/ 00036811.2018.1555321 (2018).
  18. A. Saoudi and I. A. Kallel, L2 -Uncertainty Principle for the Weinstein-Multiplier Operators, Int. J. Anal. Appl. 17 (1) (2019), 64-75.