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Fractional Fourier Transform: Main Properties and Inequalities

Author

Listed:
  • Mawardi Bahri

    (Department of Mathematics, Hasanuddin University, Makassar 90245, Indonesia)

  • Samsul Ariffin Abdul Karim

    (Software Engineering Programme, Faculty of Computing and Informatics, Universiti Malaysia Sabah, Jalan UMS, Kota Kinabalu 88400, Malaysia
    Data Technologies and Applications (DaTA) Research Group, Faculty of Computing and Informatics, Universiti Malaysia Sabah, Jalan UMS, Kota Kinabalu 88400, Malaysia)

Abstract

The fractional Fourier transform is a natural generalization of the Fourier transform. In this work, we recall the definition of the fractional Fourier transform and its relation to the conventional Fourier transform. We exhibit that this relation permits one to obtain easily the main properties of the fractional Fourier transform. We investigate the sharp Hausdorff-Young inequality for the fractional Fourier transform and utilize it to build Matolcsi-Szücs inequality related to this transform. The other versions of the inequalities concerning the fractional Fourier transform is also discussed in detail. The results obtained in this paper are very significant, especially in the field of fractional differential equations.

Suggested Citation

  • Mawardi Bahri & Samsul Ariffin Abdul Karim, 2023. "Fractional Fourier Transform: Main Properties and Inequalities," Mathematics, MDPI, vol. 11(5), pages 1-17, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1234-:d:1086838
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    References listed on IDEAS

    as
    1. Bing-Zhao Li & Tian-Zhou Xu, 2012. "Parseval Relationship of Samples in the Fractional Fourier Transform Domain," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-11, June.
    2. Sunil Kumar Singh, 2013. "The Fractional S-Transform on Spaces of Type," Journal of Mathematics, Hindawi, vol. 2013, pages 1-9, April.
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