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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Invariant subspaces of the maximal domain
of the Fourier transform


Authors: Gilbert Muraz and Pawel Szeptycki
Journal: Proc. Amer. Math. Soc. 125 (1997), 3275-3278
MSC (1991): Primary 42A38, 43A30
MathSciNet review: 1402877
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Abstract: Translation invariant subspaces of the maximal domain of the Fourier transform (the amalgam of $l^2$ with $L^1$) are characterised: it turns out that in this case all measurable subsets of the dual space are sets of spectral synthesis.


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Gilbert Muraz
Affiliation: Department of Mathematics, Institut Fourier–Grenoble, UFR-UMR 5582, BP 74, 38402 St. Martin d’Heres Cedex, France
Email: muraz@fourier.ujf-grenoble.fr

Pawel Szeptycki
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Email: szeptycki@kuhub.cc.ukans.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03973-7
PII: S 0002-9939(97)03973-7
Keywords: Fourier transform, maximal domain
Received by editor(s): August 29, 1995
Received by editor(s) in revised form: May 20, 1996
Additional Notes: Supported in part by the General Research Fund, University of Kansas
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1997 American Mathematical Society