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

K. Trim`eche, Generalized Harmonic Analysis and Wavelet Packets, Gordon and Breach Science Publishers, 2001.

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

Cover image Volume 1 issue 3

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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”, International Journal of Engineering and Applied Physics, vol. 1, no. 3, pp. 306–310, Sep. 2021.

Issue

Vol. 1 No. 3: September 2021

Section

Articles

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Copyright (c) 2021 El Mehdi LOUALID, Azzedine Achak, Radouan Daher

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