English

Generalizations of the fractional Fourier transform and their analytic properties

Classical Analysis and ODEs 2024-09-18 v1 Representation Theory

Abstract

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.

Keywords

Cite

@article{arxiv.2409.11201,
  title  = {Generalizations of the fractional Fourier transform and their analytic properties},
  author = {Yue Zhou},
  journal= {arXiv preprint arXiv:2409.11201},
  year   = {2024}
}

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22 pages