Fractional Fourier Transform: Main Properties and Inequalities

Mawardi Bahri and Samsul Ariffin Abdul Karim ()
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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

Mathematics, 2023, vol. 11, issue 5, 1-17

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.

Keywords: fractional Fourier transform; uncertainty principle; Donoho-Stark uncertainty principle (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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