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Dunkl Linear Canonical Wavelet Transform: Concentration Operators and Applications to Scalogram and Localized Functions

Author

Listed:
  • Saifallah Ghobber

    (Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia)

  • Hatem Mejjaoli

    (Department of Mathematics, College of Sciences, Taibah University, P.O. Box 30002, Al Madinah AL Munawarah 42353, Saudi Arabia)

Abstract

In the present paper we study a class of Toeplitz operators called concentration operators that are self-adjoint and compact in the linear canonical Dunkl setting. We show that a finite vector space spanned by the first eigenfunctions of such operators is of a maximal phase-space concentration and has the best phase-space concentrated scalogram inside the region of interest. Then, using these eigenfunctions, we can effectively approximate functions that are essentially localized in specific regions, and corresponding error estimates are given. These research results cover in particular the classical and the Hankel settings, and have potential application values in fields such as signal processing and quantum physics, providing a new theoretical basis for relevant research.

Suggested Citation

  • Saifallah Ghobber & Hatem Mejjaoli, 2025. "Dunkl Linear Canonical Wavelet Transform: Concentration Operators and Applications to Scalogram and Localized Functions," Mathematics, MDPI, vol. 13(12), pages 1-29, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:12:p:1943-:d:1676867
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    References listed on IDEAS

    as
    1. Navneet Kaur & Bivek Gupta & Amit K. Verma & Ravi P. Agarwal, 2024. "Offset Linear Canonical Stockwell Transform for Boehmians," Mathematics, MDPI, vol. 12(15), pages 1-18, July.
    2. Mawardi Bahri & Samsul Ariffin Abdul Karim, 2022. "Novel Uncertainty Principles Concerning Linear Canonical Wavelet Transform," Mathematics, MDPI, vol. 10(19), pages 1-17, September.
    3. Saifallah Ghobber & Hatem Mejjaoli, 2025. "A New Wavelet Transform and Its Localization Operators," Mathematics, MDPI, vol. 13(11), pages 1-32, May.
    4. Didar Urynbassarova & Aajaz A. Teali, 2023. "Convolution, Correlation, and Uncertainty Principles for the Quaternion Offset Linear Canonical Transform," Mathematics, MDPI, vol. 11(9), pages 1-24, May.
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