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Fourier transform is an isometry on some weighted Sobolev spaces
- Source :
-
Journal de Mathematiques Pures et Appliquees . Apr2013, Vol. 99 Issue 4, p489-508. 20p. - Publication Year :
- 2013
-
Abstract
- 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. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00217824
- Volume :
- 99
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Journal de Mathematiques Pures et Appliquees
- Publication Type :
- Academic Journal
- Accession number :
- 86420872
- Full Text :
- https://doi.org/10.1016/j.matpur.2012.09.010