The Fourier and Hilbert transforms under the Bargmann transform
Complex Variables
2016-05-30 v1 Functional Analysis
Abstract
There is a canonical unitary transformation from onto the Fock space , called the Bargmann transform. We study the action of the Bargmann transform on several classical integral operators on , including the fractional Fourier transform, the fractional Hilbert transform, and the wavelet transform.
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Cite
@article{arxiv.1605.08683,
title = {The Fourier and Hilbert transforms under the Bargmann transform},
author = {Xing-Tang Dong and Kehe Zhu},
journal= {arXiv preprint arXiv:1605.08683},
year = {2016}
}
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16 pages