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Deformed Wavelet Transform and Related Uncertainty Principles.
- Source :
-
Symmetry (20738994) . Mar2023, Vol. 15 Issue 3, p675. 34p. - Publication Year :
- 2023
-
Abstract
- The deformed wavelet transform is a new addition to the class of wavelet transforms that heavily rely on a pair of generalized translation and dilation operators governed by the well-known Dunkl transform. In this study, we adapt the symmetrical properties of the Dunkl Laplacian operator to prove a class of quantitative uncertainty principles associated with the deformed wavelet transform, including Heisenberg's uncertainty principle, the Benedick–Amrein–Berthier uncertainty principle, and the logarithmic uncertainty inequalities. Moreover, using the symmetry between a square integrable function and its Dunkl transform, we establish certain local-type uncertainty principles involving the mean dispersion theorems for the deformed wavelet transform. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 15
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Symmetry (20738994)
- Publication Type :
- Academic Journal
- Accession number :
- 162834487
- Full Text :
- https://doi.org/10.3390/sym15030675