| Title:
|
Dunkl-Gabor transform and time-frequency concentration (English) |
| Author:
|
Ghobber, Saifallah |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
1 |
| Year:
|
2015 |
| Pages:
|
255-270 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of this paper is to prove two new uncertainty principles for the Dunkl-Gabor transform. The first of these results is a new version of Heisenberg's uncertainty inequality which states that the Dunkl-Gabor transform of a nonzero function with respect to a nonzero radial window function cannot be time and frequency concentrated around zero. The second result is an analogue of Benedicks' uncertainty principle which states that the Dunkl-Gabor transform of a nonzero function with respect to a particular window function cannot be time-frequency concentrated in a subset of the form $S\times \mathcal B(0,b)$ in the time-frequency plane $\mathbb R^d\times \widehat {\mathbb R}^d$. As a side result we generalize a related result of Donoho and Stark on stable recovery of a signal which has been truncated and corrupted by noise. (English) |
| Keyword:
|
time-frequency concentration |
| Keyword:
|
Dunkl-Gabor transform |
| Keyword:
|
uncertainty principles |
| MSC:
|
42C20 |
| MSC:
|
43A32 |
| MSC:
|
46E22 |
| idZBL:
|
Zbl 06433733 |
| idMR:
|
MR3336037 |
| DOI:
|
10.1007/s10587-015-0172-7 |
| . |
| Date available:
|
2015-04-01T12:40:39Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144225 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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