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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.11201 |
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| _version_ | 1866912031770148864 |
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| author | Zhou, Yue |
| author_facet | Zhou, Yue |
| contents | We consider one-parameter families of quadratic-phase integral transforms which generalize the fractional Fourier transform. Under suitable regularity assumptions, we characterize the one-parameter groups formed by such transforms. Necessary and sufficient conditions for continuous dependence on the parameter are obtained in L2, pointwise, and almost-everywhere senses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11201 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalizations of the fractional Fourier transform and their analytic properties Zhou, Yue Classical Analysis and ODEs Representation Theory 42B10, 42B20, 42B25 We consider one-parameter families of quadratic-phase integral transforms which generalize the fractional Fourier transform. Under suitable regularity assumptions, we characterize the one-parameter groups formed by such transforms. Necessary and sufficient conditions for continuous dependence on the parameter are obtained in L2, pointwise, and almost-everywhere senses. |
| title | Generalizations of the fractional Fourier transform and their analytic properties |
| topic | Classical Analysis and ODEs Representation Theory 42B10, 42B20, 42B25 |
| url | https://arxiv.org/abs/2409.11201 |