The Fourier and Hilbert transforms under the Bargmann transform

Abstract

There is a canonical unitary transformation from $L^2(\mathbb{R})$ onto the Fock space $F^2$, called the Bargmann transform. We study the action of the Bargmann transform on several classical integral operators on $L^2(\mathbb{R})$, including the fractional Fourier transform, the fractional Hilbert transform, and the wavelet transform.

16 pages