[Une démonstration simple en variables réelles de la propriété d'isométrie
The Hilbert transform H can be extended to an isometry of
La transformation de Hilbert H peut être étendue à une isometrie dans
Accepté le :
Publié le :
Enrico Laeng 1
@article{CRMATH_2010__348_17-18_977_0, author = {Enrico Laeng}, title = {A simple real-variable proof that the {Hilbert} transform is an $ {L}^{2}$-isometry}, journal = {Comptes Rendus. Math\'ematique}, pages = {977--980}, publisher = {Elsevier}, volume = {348}, number = {17-18}, year = {2010}, doi = {10.1016/j.crma.2010.07.002}, language = {en}, }
Enrico Laeng. A simple real-variable proof that the Hilbert transform is an $ {L}^{2}$-isometry. Comptes Rendus. Mathématique, Volume 348 (2010) no. 17-18, pp. 977-980. doi : 10.1016/j.crma.2010.07.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.07.002/
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- Hilbert transform is an isometry: a simple proof via real rational functions, Quaestiones Mathematicae, Volume 44 (2021) no. 8, pp. 1013-1017 | DOI:10.2989/16073606.2020.1761474 | Zbl:1522.44003
- On the
norms of the Hilbert transform of a characteristic function, Journal of Functional Analysis, Volume 262 (2012) no. 10, pp. 4534-4539 | DOI:10.1016/j.jfa.2012.03.003 | Zbl:1244.42009
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