The Fourier and Hilbert transforms under the Bargmann transform

Authors: Xing-Tang Dong, Kehe Zhu

arXiv: 1605.08683v1 - DOI (math.CV)
16 pages
License: NONEXCLUSIVE-DISTRIB 1.0

Abstract: There is a canonical unitary transformation from L2(\R) onto the Fock space F2, called the Bargmann transform. We study the action of the Bargmann transform on several classical integral operators on L2(\R), including the fractional Fourier transform, the fractional Hilbert transform, and the wavelet transform.

Submitted to arXiv on 27 May. 2016

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