# 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]}^{[2]}^{[3]}

## ReferencesEdit

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