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A New Wavelet Transform and Its Localization Operators

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 define and study a new wavelet transformation associated to the linear canonical Dunkl transform (LCDT), which has been widely used in signal processing and other related fields. Then we define and study a class of pseudo-differential operators known as time-frequency (or localization) operators and we give criteria for its boundedness and Schatten class properties.

Suggested Citation

  • Saifallah Ghobber & Hatem Mejjaoli, 2025. "A New Wavelet Transform and Its Localization Operators," Mathematics, MDPI, vol. 13(11), pages 1-32, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1771-:d:1664910
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    References listed on IDEAS

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    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. Hari M. Srivastava & Azhar Y. Tantary & Firdous A. Shah & Ahmed I. Zayed, 2022. "An Interplay of Ridgelet and Linear Canonical Transforms," Mathematics, MDPI, vol. 10(12), pages 1-17, June.
    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.
    5. Hehe Yang & Qiang Feng & Xiaoxia Wang & Didar Urynbassarova & Aajaz A. Teali, 2024. "Reduced Biquaternion Windowed Linear Canonical Transform: Properties and Applications," Mathematics, MDPI, vol. 12(5), pages 1-21, March.
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    Cited by:

    1. 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.

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