Fractional Fourier Transform: Main Properties and Inequalities
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...
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| Format: | Article |
| Language: | English English |
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Molecular Diversity Preservation International (MDPI)
2023
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| Online Access: | https://eprints.ums.edu.my/id/eprint/36813/1/ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/36813/2/FULL%20TEXT.pdf |
| _version_ | 1825715340754026496 |
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| author | Mawardi Bahri Samsul Ariffin Abdul Karim |
| author_facet | Mawardi Bahri Samsul Ariffin Abdul Karim |
| author_sort | Mawardi Bahri |
| collection | UMS |
| description | 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. |
| first_indexed | 2024-03-06T03:25:23Z |
| format | Article |
| id | ums.eprints-36813 |
| institution | Universiti Malaysia Sabah |
| language | English English |
| last_indexed | 2024-03-06T03:25:23Z |
| publishDate | 2023 |
| publisher | Molecular Diversity Preservation International (MDPI) |
| record_format | dspace |
| spelling | ums.eprints-368132023-09-18T03:22:17Z https://eprints.ums.edu.my/id/eprint/36813/ Fractional Fourier Transform: Main Properties and Inequalities Mawardi Bahri Samsul Ariffin Abdul Karim QA299.6-433 Analysis TK5101-6720 Telecommunication Including telegraphy, telephone, radio, radar, television 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. Molecular Diversity Preservation International (MDPI) 2023 Article NonPeerReviewed text en https://eprints.ums.edu.my/id/eprint/36813/1/ABSTRACT.pdf text en https://eprints.ums.edu.my/id/eprint/36813/2/FULL%20TEXT.pdf Mawardi Bahri and Samsul Ariffin Abdul Karim (2023) Fractional Fourier Transform: Main Properties and Inequalities. Mathematics, 11. pp. 1-17. https://doi.org/10.3390/math11051234 |
| spellingShingle | QA299.6-433 Analysis TK5101-6720 Telecommunication Including telegraphy, telephone, radio, radar, television Mawardi Bahri Samsul Ariffin Abdul Karim Fractional Fourier Transform: Main Properties and Inequalities |
| title | Fractional Fourier Transform: Main Properties and Inequalities |
| title_full | Fractional Fourier Transform: Main Properties and Inequalities |
| title_fullStr | Fractional Fourier Transform: Main Properties and Inequalities |
| title_full_unstemmed | Fractional Fourier Transform: Main Properties and Inequalities |
| title_short | Fractional Fourier Transform: Main Properties and Inequalities |
| title_sort | fractional fourier transform main properties and inequalities |
| topic | QA299.6-433 Analysis TK5101-6720 Telecommunication Including telegraphy, telephone, radio, radar, television |
| url | https://eprints.ums.edu.my/id/eprint/36813/1/ABSTRACT.pdf https://eprints.ums.edu.my/id/eprint/36813/2/FULL%20TEXT.pdf |
| work_keys_str_mv | AT mawardibahri fractionalfouriertransformmainpropertiesandinequalities AT samsulariffinabdulkarim fractionalfouriertransformmainpropertiesandinequalities |