English

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 L2(R)L^2(\R) onto the Fock space F2F^2, called the Bargmann transform. We study the action of the Bargmann transform on several classical integral operators on L2(R)L^2(\R), including the fractional Fourier transform, the fractional Hilbert transform, and the wavelet transform.

Keywords

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}
}

Comments

16 pages

R2 v1 2026-06-22T14:11:19.531Z