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Fourier-Stieltjes algebra of a groupoid (Definition)
Definition 0.1   The Fourier-Stieltjes algebra of a groupoid, $G_l$. In ref. [3]), A.L.T. Paterson defined the Fourier-Stieltjes algebra of a groupoid, $G_l$, as the space of coefficients $\phi = (\xi,\eta)$, where $\xi,\eta$ are $L^{\infty}$-sections for some measurable $G_l$ -Hilbert bundle $(\mu,\Re,L)$. Thus, for $x \in G_l$,
$\displaystyle \phi(x) = L(x) \xi (s(x),\eta (r(x))).$ (0.1)

Therefore, $\phi$ belongs to $L^\infty{G_l} = L^\infty({G_l},\nu)$.

Bibliography

1
A. Ramsay and M. E. Walter, Fourier-Stieltjes algebras of locally compact groupoids, J. Functional Anal. 148: 314-367 (1997).
2
A. L. T. Paterson, The Fourier algebra for locally compact groupoids., Preprint, (2001).
3
A. L. T. Paterson, The Fourier-Stieltjes and Fourier algebras for locally compact groupoids, (2003).



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This is version 3 of Fourier-Stieltjes algebra of a groupoid, born on 2010-06-04, modified 2010-06-04.
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Classification:
Physics Classification: 00. (GENERAL)
 02. (Mathematical methods in physics)
 02.70.-cxx (Computational techniques )
 02.90.+p (Other topics in mathematical methods in physics )
Pending Errata and Addenda
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