L2 -Uncertainty Principle for the Weinstein-Multiplier Operators

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Ahmed Saoudi, Imen Ali Kallel

Abstract

The aim of this paper is establish the Heisenberg-Pauli-Weyl uncertainty principle and DonhoStark's uncertainty principle for the Weinstein L2 -multiplier operators.

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References

  1. J.P. Anker, Lp Fourier multipliers on Riemannian symmetric spaces of the noncompact type, Ann. Math. (2). 132(3) (1990), 597-628.
  2. N. Ben Salem and AR. Nasr, Heisenberg-type inequalities for the Weinstein operator, Integral Transforms Spec. Funct. 26(9) (2015), 700-718.
  3. 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. Anal. 242(1) (2007), 327-336.
  4. M. Brelot, Equation de Weinstein et potentiels de Marcel Riesz, Semin. Theor. Potent., Paris, No. 3, Lect. Notes Math. 3 (1978), 18-38.
  5. D.L.Donoho and P.B. Stark, Uncertainty principles and signal recovery, SIAM J. Appl. Math. 49(3) (1989), 906931.
  6. J. Gosselin and K. Stempak, A weak-type estimate for Fourier-Bessel multipliers, Proc. Amer. Math. Soc. 106(3) (1989), 655-662.
  7. G. Kimeldorf and G. Wahba, Some results on Tchebycheffian spline functions and stochastic processes, J. Math. Anal. Appl. 33(1) (1971), 82-95.
  8. 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.
  9. H. Mejjaoli and M. Salhi, Uncertainty principles for the Weinstein transform, Czech. Math. J. 61 (2011), 941-974.
  10. H. Ben Mohamed and B. Ghribi, Weinstein-Sobolev spaces of exponential type and applications, Acta Math. Sin., Engl. Ser. 29 (3) (2013), 591-608.
  11. Z. Ben Nahia and N. Ben Salem, On a mean value property associated with the Weinstein operator, Potential theory - ICPT '94. Proceedings of the international conference, Kouty, Czech Republic, Berlin: de Gruyter (1996), 243-253.
  12. Z. Ben Nahia and N. Ben Salem, Spherical harmonics and applications associated with the Weinstein operator, Potential theory - ICPT '94. Proceedings of the international conference, Kouty, Czech Republic, Berlin: de Gruyter (1996), 233-241.
  13. A. Nowak and K. Stempak, Relating transplantation and multipliers for Dunkl and Hankel transforms, Math. Nachr. 281(11) (2008), 1604-1611.
  14. A. Saoudi, Calder ´on's reproducing formulas for the Weinstein L2 -multiplier operators, arXiv:1801.08939 [math.AP].
  15. S.Saitoh, Approximate real inversion formulas of the gaussian convolution, Appl. Anal. 83(7) (2004), 727-733.
  16. F. Soltani, Lp-Fourier multipliers for the Dunkl operator on the real line, J. Funct. Anal. 209(1) (2004), 16-35.
  17. F. Soltani, Multiplier operators and extremal functions related to the dual Dunkl-Sonine operator, Acta Math. Sci., Ser. B, Engl. Ed. 33(2) (2013), 430-442.
  18. F. Soltani, Dunkl multiplier operators on a class of reproducing kernel Hilbert spaces. J. Math. Res. Appl. 36(6) (2016), 689-702.