| Title:
|
A dispersion inequality in the Hankel setting (English) |
| Author:
|
Ghobber, Saifallah |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
68 |
| Issue:
|
1 |
| Year:
|
2018 |
| Pages:
|
227-241 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
time-frequency concentration |
| Keyword:
|
windowed Hankel transform |
| Keyword:
|
Shapiro's uncertainty principles |
| MSC:
|
42C20 |
| MSC:
|
45P05 |
| MSC:
|
94A12 |
| idZBL:
|
Zbl 06861577 |
| idMR:
|
MR3783595 |
| DOI:
|
10.21136/CMJ.2018.0445-16 |
| . |
| Date available:
|
2018-03-19T10:29:41Z |
| Last updated:
|
2020-07-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147131 |
| . |
| Reference:
|
[1] Bowie, P. C.: Uncertainty inequalities for Hankel transforms.SIAM J. Math. Anal. 2 (1971), 601-606. Zbl 0235.44002, MR 0304983, 10.1137/0502059 |
| Reference:
|
[2] Czaja, W., Gigante, G.: Continuous Gabor transform for strong hypergroups.J. Fourier Anal. Appl. 9 (2003), 321-339. Zbl 1037.42031, MR 1999563, 10.1007/s00041-003-0017-x |
| Reference:
|
[3] Ghobber, S.: Phase space localization of orthonormal sequences in $L_\alpha^2(\Bbb R_+)$.J. Approx. Theory 189 (2015), 123-136. Zbl 1303.42015, MR 3280675, 10.1016/j.jat.2014.10.008 |
| Reference:
|
[4] Ghobber, S., Omri, S.: Time-frequency concentration of the windowed Hankel transform.Integral Transforms Spec. Funct. 25 (2014), 481-496. Zbl 1293.42005, MR 3172059, 10.1080/10652469.2013.877009 |
| Reference:
|
[5] Lamouchi, H., Omri, S.: Time-frequency localization for the short time Fourier transform.Integral Transforms Spec. Funct. 27 (2016), 43-54. Zbl 1334.42022, MR 3417389, 10.1080/10652469.2015.1092439 |
| Reference:
|
[6] Levitan, B. M.: Expansion in Fourier series and integrals with Bessel functions.Uspekhi Matem. Nauk (N.S.) 6 (1951), 102-143 Russian. Zbl 0043.07002, MR 0049376 |
| Reference:
|
[7] Malinnikova, E.: Orthonormal sequences in $L^2(\Bbb R^d)$ and time frequency localization.J. Fourier Anal. Appl. 16 (2010), 983-1006. Zbl 1210.42020, MR 2737766, 10.1007/s00041-009-9114-9 |
| Reference:
|
[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. |
| . |
