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- W2092422582 abstract "We show that, under adequate norms, the Fourier transform is an isometry over a chain of nested weighted Sobolev spaces. As a result, an infinite number of useful Plancherel-like identities are derived. Possible extensions are discussed, giving rise to some open questions. Dans cet article, on démontre que la transformation de Fourier est une isométrie de certains espaces de Sobolev à poids, pourvu que la norme soit convenablement choisie. On en déduit en particulier une infinité dʼidentités de type Plancherel pour des normes pondérées. Quelques extensions possibles de ces résulats ainsi que des questions ouvertes associées sont discutées." @default.
- W2092422582 created "2016-06-24" @default.
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- W2092422582 date "2013-04-01" @default.
- W2092422582 modified "2023-10-10" @default.
- W2092422582 title "Fourier transform is an isometry on some weighted Sobolev spaces" @default.
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- W2092422582 doi "https://doi.org/10.1016/j.matpur.2012.09.010" @default.
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