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The Fourier and Hilbert transforms under the Bargmann transform (1605.08683v1)
Published 27 May 2016 in math.CV and math.FA
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.
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