The aim of this paper is to prove another variation on the Heisenberg uncertainty principle, we generalize the quantitative uncertainty relations in $n$ different (time-frequency) domains and we will give an algorithm for the signal recovery related to the canonical Fourier-Bessel transform.
Jihed SAHBANI
,
Lazhar DHAOUADI
. UNCERTAINTY PRINCIPLES AND SIGNAL RECOVERY RELATED TO THE CANONICAL FOURIER-BESSEL TRANSFORM[J]. Acta mathematica scientia, Series B, 2025
, 45(5)
: 2190
-2207
.
DOI: 10.1007/s10473-025-0520-0
[1] Benedicks M. On Fourier transforms of function supported on sets of finite Lebesgue measure. J Math Anal Appl, 1985, 106: 180-183
[2] Beurling A.The Collected Works of Arne Beurling. Vol 1-2. Boston: Birkhäuser, 1989
[3] Dhaouadi L, Sahbani J, Fitouhi A. Harmonic analysis associated to the canonical Fourier Bessel transform. Integral Transforms and Special Functions, 2021, 32(4): 290-315
[4] Donoho D, Stark P. Uncertainty principles and signal recovery. SIAM J Appl Math, 1989, 49: 906-931
[5] Folland G B, Sitaram A. The uncertainty principle: A mathematical survey. J Fourier Anal Appl, 1997, 3(3): 207-238
[6] Ghazouani S, Sahbani J. Canonical Fourier-Bessel transform and their applications. J Pseudo-Differ Oper Appl, 2023, 14: Art 3
[7] Ghazouani S, Soltani E, Fitouhi A. A unified class of integral transforms related to the Dunkl transform. J Math Anal Appl, 2017, 449(2): 1797-1849
[8] Healy J J, Kutay M A, Ozaktas H M, Sheridan J T.Linear Canonical Transforms: Theory and Applications. New York: Springer, 2016
[9] Hörmander L. A uniqueness theorem of Beurling for Fourier transform pairs. Arkiv fur Matematik, 1991, 29: 237-240
[10] Kerr F. A fractional power theory for Hankel transforms in $L^{2}(\mathbb{R}_{+})$. J Math Anal Appl, 1991, 158(1): 114-123
[11] Landau H J, Pollak H O. Prolate spheroidal wave functions, Fourier analysis and uncertainty II. Bell Syst Tech J, 1961, 40: 65-84
[12] Moshinsky M, Quesne C. Linear canonical transformations and their unitary representations. J Mathematical Phys, 1971, 12: 1772-1780
[13] Quesne C, Moshinsky M. Canonical transformations and matrix elements. J Math Phys, 1971, 12: 1780-1783
[14] Sahbani J, Guettiti T. Prolate spheroidal wave functions associated with the canonical Fourier-Bessel transform and uncertainty principles. Math Meth Appl Sci, 2023, 46(14): 15506-15525
[15] Sahbani J. Quantitative uncertainty principles for the canonical Fourier-Bessel transform. Acta Mathematica Sinica, 2022, 38(2): 331-346
[16] Stuart A, Collins J. Lens-system diffraction integral written in terms of matrix optics. Journal of the Optical Society of America, 1970, 60(9): 1168-1177
[17] Tuan V K. Uncertainty principles for the Hankel transform. Integral Transforms and Special Functions, 2007, 18(5): 369-381
[18] Watson G.A Treatise on the Theory of Bessel Functions. Cambridge: Cambridge University Press, 1944
