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# The Fourier Algebra for Locally Compact Groupoids

Published:2004-12-01
Printed: Dec 2004
• Alan L. T. Paterson
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## Abstract

We introduce and investigate using Hilbert modules the properties of the {\em Fourier algebra} $A(G)$ for a locally compact groupoid $G$. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This includes as a special case the classical duality theorem for locally compact groups proved by P. Eymard.
 Keywords: Fourier algebra, locally compact groupoids, Hilbert modules, positive definite functions, completely bounded maps
 MSC Classifications: 43A32 - Other transforms and operators of Fourier type