Uncertainty Principles for the Weinstein Wavelet Transform
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Abstract
In the present paper we explore the localization properties of the Weinstein continuous wavelet transform via entropy and we introduce a version of Lp local uncertainty inequalities.
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References
- H.B. Mohamed, Y. Bettaibi, Pseudo-Differential Operators in the Generalized Weinstein Setting, Rend. Circ. Mat. Palermo, II. Ser. 72 (2023), 3345–3361. https://doi.org/10.1007/s12215-022-00827-7.
- C. Chettaoui, H.B. Mohamed, Bochner–Hecke Theorems in the Generalized Weinstein Theory Setting, Complex Anal. Oper. Theory 17 (2023), 38. https://doi.org/10.1007/s11785-023-01342-y.
- A. Gasmi, H. Ben Mohamed, N. Bettaibi, Inversion of Weinstein intertwining operator and its dual using Weinstein wavelets, An. Univ. "Ovidius" Constant,a, Ser. Mat. 24 (2016), 289–307. https://doi.org/10.1515/auom-2016-0016.
- I. Kallel, A. Saoudi, Uncertainty Principle for the Weinstein-Gabor Transforms, Int. J. Anal. Appl. 22 (2024), 94. https://doi.org/10.28924/2291-8639-22-2024-94.
- H. Mejjaoli, A. Ould Ahmed Salem, New Results on the Continuous Weinstein Wavelet Transform, J. Inequal. Appl. 2017 (2017), 270. https://doi.org/10.1186/s13660-017-1534-5.
- H.B. Mohamed, A. Saoudi, Linear Canonical Fourier–Bessel Wavelet Transform: Properties and Inequalities, Integr. Transforms Spec. Funct. 35 (2024), 270–290. https://doi.org/10.1080/10652469.2024.2317724.
- Z.B. Nahia, Fonctions Harmoniques et Proprietés de la Moyenne Associées à l’Opérateur de Weinstein, Thesis, Department of Mathematics, Faculty of Sciences of Tunis, Tunisia, 1995.
- N.B. Salem, Inequalities Related to Spherical Harmonics Associated With the Weinstein Operator, Integr. Transforms Spec. Funct. 34 (2022), 41–64. https://doi.org/10.1080/10652469.2022.2087063.
- N.B. Salem, A.R. Nasr, Heisenberg-Type Inequalities for the Weinstein Operator, Integr. Transforms Spec. Funct. 26 (2015), 700–718. https://doi.org/10.1080/10652469.2015.1038531.
- A. Saoudi, On the Weinstein–Wigner Transform and Weinstein–Weyl Transform, J. Pseudo-Differ. Oper. Appl. 11 (2020), 1–14. https://doi.org/10.1007/s11868-019-00313-2.
- A. Saoudi, A Variation of L p Uncertainty Principles in Weinstein Setting, Indian J. Pure Appl. Math. 51 (2020), 1697–1712. https://doi.org/10.1007/s13226-020-0490-9.
- A. Saoudi, Two-Wavelet Theory in Weinstein Setting, Int. J. Wavelets Multiresolut. Inf. Process. 20 (2022), 2250020. https://doi.org/10.1142/S0219691322500205.
- A. Saoudi, Time-Scale Localization Operators in the Weinstein Setting, Results Math. 78 (2022), 14. https://doi.org/10.1007/s00025-022-01792-4.
- A. Saoudi, Hardy Type Theorems for Linear Canonical Dunkl Transform, Complex Anal. Oper. Theory 18 (2024), 57. https://doi.org/10.1007/s11785-023-01478-x.
- A. SAOUDI, I. KALLEL, A Variation of L p Local Uncertainty Principles for Weinstein Transform, Proc. Rom. Acad. Ser. A - Math. Phys. Tech. Sci. Inf. Sci. 25 (2024), 3–10. https://doi.org/10.59277/pra-ser.a.25.1.01.
- A. Saoudi, B. Nefzi, Boundedness and Compactness of Localization Operators for Weinstein–Wigner Transform, J. Pseudo-Differ. Oper. Appl. 11 (2020), 675–702. https://doi.org/10.1007/s11868-020-00328-0.
- M. Sartaj, S.K. Upadhyay, Symmetrically Global Pseudo-Differential Operators Involving the Weinstein Transform, J. Pseudo-Differ. Oper. Appl. 14 (2023), 51. https://doi.org/10.1007/s11868-023-00543-5.
- D. Slepian, Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - IV: Extensions to Many Dimensions; Generalized Prolate Spheroidal Functions, Bell Syst. Techn. J. 43 (1964), 3009–3057. https://doi.org/10.1002/j.1538-7305.1964.tb01037.x.
- H.M. Srivastava, S. Yadav, S.K. Upadhyay, The Weinstein Transform Associated With a Family of Generalized Distributions, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117 (2023), 132. https://doi.org/10.1007/s13398-023-01461-3.
- S.K. Upadhyay, M. Sartaj, An Integral Representation of Pseudo-Differential Operators Involving Weinstein Transform, J. Pseudo-Differ. Oper. Appl. 13 (2022), 33. https://doi.org/10.1007/s11868-022-00442-1.