Hardy’s theorem for the generalized Bessel transform on the half line

Authors

  • El Mehdi Loualid Laboratory of Engineering Sciences for Energy National School of Applied Sciences University Chouaib Doukkali https://orcid.org/0000-0002-2915-1772
  • Azzedine Achak Higher School of Education and Formation. University Chouaib Doukkali, El Jadida Morocco
  • Radouan Daher Department of Mathematics, Faculty of Sciences Ain Chock, University of Hassan II, Casablanca, Morocco

Keywords:

Generalized Bessel transform, Uncertainty principle, Hardy's theorem

Abstract

In this paper, we give a generalization of a qualitative uncertainty principle namely Hardy’s theorem, which asserts that a function and its Fourier transform cannot both be very small, for the generalized Bessel transform on the half line.

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References

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R.F. Al Subaie and M.A. Mourou, Transmutation operators associated with a Bessel type operator on the half line and certain of their applications, to appear in Tamsui Oxford Journal of Mathematics.

Hardy G H. A theorem concerning Fourier transforms. J London Math Soc, 1933, 8: 227-231

Hardy, G., 1933, A theorem concerning Fourier transform, Journal of the London Mathematical Society, 8, 227231.

Huang J and Liu H, A heat kernel version of Hardy’s theorem for the Laguerre hypergroup. Acta Mathematica Scientia 2011,31B(2):451-458

Thangavelu S. An introduction to the uncertainty principle. Progr Math Vol. 217. Boston-Basel-Berlin: Birkhauser, 2003

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Thangavelu S. An introduction to the uncertainty principle. Progr Math Vol. 217. Boston-Basel-Berlin: Birkhauser, 2003

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Published

2021-09-25

How to Cite

[1]
E. M. Loualid, A. . Achak, and R. Daher, “Hardy’s theorem for the generalized Bessel transform on the half line”, Int J Eng and Appl Phys, vol. 1, no. 3, pp. 306–310, Sep. 2021.

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