Science in China Series A: Mathematics

, Volume 47, Issue 3, pp 393–400 | Cite as

Wavelets associated with Hankel transform and their Weyl transforms



The Hankel transform is an important transform. In this paper, we study the wavelets associated with the Hankel transform, then define the Weyl transform of the wavelets. We give criteria of its boundedness and compactness on the L p — spaces.


Bessel function Hankel transform wavelets Weyl transform boundedness compactness 


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  1. 1.
    Weyl, H., The Theory of Groups and Quantum Mechanics, New York: Dover, 1931.MATHGoogle Scholar
  2. 2.
    Pool, J. C. T., Mathematical aspect of the Weyl correspondence, J. Math. Phys., 1966, 7: 66–76.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Simon, B., The Weyl transform and L p functions on phase space, Proc. Amer. Math. Soc., 1992, 116: 1045–1047.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Wong, M. W., Weyl Transform, New York: Springer-Verlag, 1998.Google Scholar
  5. 5.
    Jiang, Q., Rotation Invariant ambiguity functions, Proc. Amer. Math. Soc., 1996, 126(2): 561–567.CrossRefGoogle Scholar
  6. 6.
    Rachdi, L. T., Trimeche, K., Weyl transforms associated with the spherical mean operator, Anal. & Applic., (to appear).Google Scholar
  7. 7.
    Peng, L. Z., Zhao, J. M., Wavelet and Weyl transforms associated with spherical mean operator, Integral Equations and Operator Theory, (to appear).Google Scholar
  8. 8.
    Ma, R. Q., Peng, L. Z., Weyl transforms of wavelets, Progress on Natural Science, 2003, 13(7): 489–496.MathSciNetGoogle Scholar
  9. 9.
    Azza Dachraoui, Weyl-Bessel transforms, J. Comput. Appl. Math., 2001, 133: 263–276.MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Stein, E. M., Weiss, G., Introduction to Fourier Analysis on Euclidean Spaces, Princeton: Princeton University Press, 1971.MATHGoogle Scholar
  11. 11.
    Watson, G. N., A Treatise on the Theory of Bessel Functions, London and New-York: Cambridge University Press, 1966.MATHGoogle Scholar
  12. 12.
    Vilenkin, N. Ja., Klimyk, A. U., Representation of Lie Groups and Special Functions, Dordrecht: Kluwer Academic Publishers, 1991.MATHGoogle Scholar
  13. 13.
    Daubechies, I., Ten lectures on wavelet, CBMS-NSF Series in Applied Math, 61, SIAM Publ., 1992.Google Scholar

Copyright information

© Science in China Press 2004

Authors and Affiliations

  1. 1.LMAM, School of Mathematical SciencesPeking UniversityBeijingChina

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