Towards a dictionary for the Bargmann transform

2015/06/21 by Kehe Zhu, Zhu, Kehe
Computer Science · Earth and Planetary Sciences · Mathematics · #30H20 #Digital Filter Design and Implementation #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Seismic Imaging and Inversion Techniques #math.FA #msc:30H20

paper · pdf · doi:10.48550/arxiv.1506.06326

arxiv created 2015/06/21 · openalex publication_date 2015/06/21 · arxiv updated 2015/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

There is a canonical unitary transformation from L²(\R) onto the Fock space F², called the Bargmann transform. The purpose of this article is to translate some important results and operators from the context of L²(\R) to that of F². Examples include the Fourier transform, the Hilbert transform, Gabor frames, pseudo-differential operators, and the uncertainty principle.

Related

• The Fourier and Hilbert transforms under the Bargmann transform
• Canonical integral operators on the Fock space
• The Segal-Bargmann Transform in Clifford Analysis
• Fourier multipliers and pseudo-differential operators on Fock-Sobolev spaces
• On composition of Segal-Bargmann transforms