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Journal of the London Mathematical Society Advance Access originally published online on April 18, 2007
Journal of the London Mathematical Society 2007 75(2):369-390; doi:10.1112/jlms/jdm002
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© 2007 London Mathematical Society

Multipliers on Banach spaces of functions on a locally compact Abelian group

Violeta Petkova

Laboratoire Bordelais d’Analyse et Géométrie
UMR 5467
Université Bordeaux 1
351, cours de la Libération
33405 Talence
France

Let E be a Banach space of functions on a locally compact Abelian group G satisfying certain conditions. It has been proved that for every bounded operator M on E commuting with translations there exists Formula such that Formula, where Formula is a suitable subset of the group of the continuous morphisms from G into C* and Formula is a generalized Fourier transform of g defined on Formula.

petkova{at}math.u-bordeaux1.fr

2000 Mathematics Subject Classification 43A22, 43A25.

Received January 6, 2006; published online April 18, 2007.


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