Fourier-Stieltjes algebra of a groupoid

Definition 0.1.

The Fourier-Stieltjes algebra of a groupoidPlanetmathPlanetmathPlanetmath, Gl. In ref. [3]), A.L.T. Paterson defined the Fourier-Stieltjes algebra of a groupoid, Gl, as the space of coefficients ϕ=(ξ,η), where ξ,η are
L-sectionsPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath for some measurable Gl -Hilbert bundle (μ,,L). Thus, for xGl,

ϕ(x)=L(x)ξ(s(x),η(r(x))). (0.1)

Therefore, ϕ belongs to LGl=L(Gl,ν).


  • 1 A. Ramsay and M. E. Walter, Fourier-Stieltjes algebras of locally compact groupoidsPlanetmathPlanetmath, J. FunctionalMathworldPlanetmathPlanetmathPlanetmath 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