PlanetPhysics/Generalized Fourier Transform

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Fourier-Stieltjes TransformEdit

Given a positive definite, measurable function   on the interval   there exists a monotone increasing, real-valued bounded function   such that:


for all   except a `small' set, that is a finite set which contains only a small number of values. When   is defined as above and if   is nondecreasing and bounded then the measurable function defined by the above integral is called the Fourier-Stieltjes transform of  , and it is continuous in addition to being positive definite .

All SourcesEdit



  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).