Fourier transform is an isometry on some weighted Sobolev spaces

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. (C) 2012 Elsevier Masson SAS. All rights reserved.
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Tahar Z. Boulmezaoud. Fourier transform is an isometry on some weighted Sobolev spaces. Journal de Mathématiques Pures et Appliquées, Elsevier, 2013, 99 (4), pp.489-508. ⟨10.1016/j.matpur.2012.09.010⟩. ⟨hal-02166376⟩

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