Fourier-Stieltjes algebra of a groupoid

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 $x\in G_{l}$ ,

\phi(x)=L(x)\xi(s(x),\eta(r(x))).

(0.1)

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

References

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).

Title	Fourier-Stieltjes algebra of a groupoid
Canonical name	FourierStieltjesAlgebraOfAGroupoid
Date of creation	2013-03-22 18:16:11
Last modified on	2013-03-22 18:16:11
Owner	bci1 (20947)
Last modified by	bci1 (20947)
Numerical id	11
Author	bci1 (20947)
Entry type	Definition
Classification	msc 55N33
Classification	msc 55N20
Classification	msc 55P10
Classification	msc 55U40
Classification	msc 42B10
Classification	msc 42A38
Classification	msc 43A25
Classification	msc 43A30
Synonym	Fourier-Stieltjes algebra of a groupoid
Related topic	FourierStieltjesTransform
Related topic	Distribution4
Defines	Fourier-Stieltjes algebra