Calderón’s reproducing formula and uncertainty principle for the continuous wavelet transform associated with the q-Bessel operator

被引：0
作者：
Bochra Nefzi
Kamel Brahim
机构：
[1] University of Tunis El Manar,Faculty of Sciences of Tunis
来源：
Journal of Pseudo-Differential Operators and Applications | 2018年 / 9卷
关键词：
-Wavelet; Continuous ; -wavelet transform; -Bessel operator; -Bessel Fourier transform; Calderón’s reproducing formula; Uncertainty principle; Heisenberg–Pauli–Weyl inequality; 33B15; 33D05; 44A20; 42A38; 42B10;
D O I：
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学科分类号：
摘要：
In this paper, we present some new elements of harmonic analysis related to the q-Bessel Fourier transform introduced earlier in Dhaouadi (Bull Math Anal Appl 5(2):42–60, 2013), Dhaouadi et al. (J Inequal Pure Appl Math 7(5):171, 2006), we define and study the q-wavelet and the continuous q-wavelet transform associated with this harmonic analysis. Thus, some results (Plancherel’s formula, inversion formula, etc.) are established. Next, we prove a Calderón’s formula and an analogue of Heisenberg’s inequality for the continuous q-wavelet transform.
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页码：495 / 522
页数：27
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