The Fourier and Hilbert transforms Under the Bargmann transform

DOI10.1080/17476933.2017.1324430zbMath1394.30041arXiv1605.08683OpenAlexW2962757599MaRDI QIDQ5374206

Xing-Tang Dong, K. H. Zhu

Publication date: 9 April 2018

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.08683

zbMATH Keywords

wavelet transformFock spacefractional Fourier transformfractional Hilbert transformBargmann transform

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Bergman spaces and Fock spaces (30H20)

Related Items (5)

Characterizations of Bounded Singular Integral Operators on the Fock Space and Their Berezin Transforms ⋮ Canonical integral operators on the Fock space ⋮ Spectrum of normal weighted composition operators on the Fock space over \(\mathbb{C}^N\) ⋮ Numerical ranges of normal weighted composition operators on the Fock space of \(\mathbb{C}^N\) ⋮ A boundedness criterion for singular integral operators of convolution type on the Fock space

Cites Work

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• Recent developments in the theory of the fractional Fourier and linear canonical transforms
• Foundations of time-frequency analysis
• Singular integral operators on the Fock space
• Analysis on Fock Spaces
• On a Hilbert space of analytic functions and an associated integral transform part I
• Harmonic Analysis in Phase Space. (AM-122)
• Heat Flow and Berezin-Toeplitz Estimates
• On a Hilbert Space of Analytie Functions and an Associated Integral Transform. Part II. A Family of Related Function Spaces Application to Distribution Theory

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