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Keywords:
time-frequency concentration; windowed Hankel transform; Shapiro's uncertainty principles
Summary:
The aim of this paper is to prove a quantitative version of Shapiro's uncertainty principle for orthonormal sequences in the setting of Gabor-Hankel theory.
References:
[1] Bowie, P. C.: Uncertainty inequalities for Hankel transforms. SIAM J. Math. Anal. 2 (1971), 601-606. DOI 10.1137/0502059 | MR 0304983 | Zbl 0235.44002
[2] Czaja, W., Gigante, G.: Continuous Gabor transform for strong hypergroups. J. Fourier Anal. Appl. 9 (2003), 321-339. DOI 10.1007/s00041-003-0017-x | MR 1999563 | Zbl 1037.42031
[3] Ghobber, S.: Phase space localization of orthonormal sequences in $L_\alpha^2(\Bbb R_+)$. J. Approx. Theory 189 (2015), 123-136. DOI 10.1016/j.jat.2014.10.008 | MR 3280675 | Zbl 1303.42015
[4] Ghobber, S., Omri, S.: Time-frequency concentration of the windowed Hankel transform. Integral Transforms Spec. Funct. 25 (2014), 481-496. DOI 10.1080/10652469.2013.877009 | MR 3172059 | Zbl 1293.42005
[5] Lamouchi, H., Omri, S.: Time-frequency localization for the short time Fourier transform. Integral Transforms Spec. Funct. 27 (2016), 43-54. DOI 10.1080/10652469.2015.1092439 | MR 3417389 | Zbl 1334.42022
[6] Levitan, B. M.: Expansion in Fourier series and integrals with Bessel functions. Uspekhi Matem. Nauk (N.S.) 6 (1951), 102-143 Russian. MR 0049376 | Zbl 0043.07002
[7] Malinnikova, E.: Orthonormal sequences in $L^2(\Bbb R^d)$ and time frequency localization. J. Fourier Anal. Appl. 16 (2010), 983-1006. DOI 10.1007/s00041-009-9114-9 | MR 2737766 | Zbl 1210.42020
[8] Shapiro, H. S.: Uncertainty principles for basis in $L^2(\mathbb R)$. Proc. of the Conf. on Harmonic Analysis and Number Theory, Marseille-Luminy, 2005 CIRM.
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