The Hilbert transform and Hermite functions: a real variable proof of the \(L^2\)-isometry

DOI10.1016/j.jmaa.2008.06.016zbMath1153.44003OpenAlexW2015949733MaRDI QIDQ944353

Javier Duoandikoetxea

Publication date: 16 September 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2008.06.016

zbMATH Keywords

Hilbert transformisometryHermite functions

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Isometric theory of Banach spaces (46B04)

Related Items (4)

The bilinear Hilbert transform acting on Hermite and Laguerre functions ⋮ Hilbert transform is an isometry: A simple proof via real rational functions ⋮ A simple real-variable proof that the Hilbert transform is an \(L^{2}\)-isometry ⋮ On singularity formation of a nonlinear nonlocal system

Cites Work

• On a theorem of Akhiezer
• Computing the Hilbert transform of the generalized Laguerre and Hermite weight functions
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