Hilbert transform is an isometry: A simple proof via real rational functions

DOI10.2989/16073606.2020.1761474OpenAlexW3033430818MaRDI QIDQ5163028

Shirley Bromberg-Silverstein, Omar Sanchez Antonio, Victor A. Cruz Barriguete

Publication date: 8 November 2021

Published in: Quaestiones Mathematicae (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10261/261602

zbMATH Keywords

Hilbert transformrational functions

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Integral transforms of special functions (44A20) Real rational functions (26C15)

Cites Work

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• A simple real-variable proof that the Hilbert transform is an \(L^{2}\)-isometry
• The Hilbert transform and Hermite functions: a real variable proof of the \(L^2\)-isometry
• Classical Fourier Analysis
• A Complete Orthonormal System of Functions in $L^2 ( - \infty ,\infty )$ Space

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