Uncertainty Principles for the Weinstein Wavelet Transform

Main Article Content

Amel Touati, Imen Kallel, Ahmed Saoudi

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.

Article Details

References

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. A. Saoudi, Two-Wavelet Theory in Weinstein Setting, Int. J. Wavelets Multiresolut. Inf. Process. 20 (2022), 2250020. https://doi.org/10.1142/S0219691322500205.
  13. A. Saoudi, Time-Scale Localization Operators in the Weinstein Setting, Results Math. 78 (2022), 14. https://doi.org/10.1007/s00025-022-01792-4.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.