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Uncertainty Principles for the Continuous Dunkl Gabor Transform and the Dunkl Continuous Wavelet Transform
- Source :
- Mediterranean Journal of Mathematics. 5:443-466
- Publication Year :
- 2008
- Publisher :
- Springer Science and Business Media LLC, 2008.
-
Abstract
- In this paper we consider the Dunkl operators Tj, j = 1, . . . , d, on \(\mathbb {R}^d\) and the harmonic analysis associated with these operators. We define a continuous Dunkl Gabor transform, involving the Dunkl translation operator, by proceeding as mentioned in [20] by C.Wojciech and G. Gigante. We prove a Plancherel formula, an \(L^2_{k}\) inversion formula and a weak uncertainty principle for it. Then, we show that the portion of the continuous Dunkl Gabor transform lying outside some set of finite measure cannot be arbitrarily too small. Similarly, using the basic theory for the Dunkl continuous wavelet transform introduced by K. Trimeche in [18], an analogous of this result for the Dunkl continuous wavelet transform is given. Finally, an analogous of Heisenberg’s inequality for a continuous Dunkl Gabor transform (resp. Dunkl continuous wavelet transform) is proved.
- Subjects :
- Pure mathematics
Uncertainty principle
General Mathematics
Mathematical analysis
Mathematics::Classical Analysis and ODEs
Gabor transform
Translation operator
Wavelet
Mathematics::Quantum Algebra
Mathematics::Representation Theory
Harmonic wavelet transform
S transform
Continuous wavelet transform
Dunkl operator
Mathematics
Subjects
Details
- ISSN :
- 16605454 and 16605446
- Volume :
- 5
- Database :
- OpenAIRE
- Journal :
- Mediterranean Journal of Mathematics
- Accession number :
- edsair.doi...........ee5ee7d2d106a75f7162f5ca122f36ac