PlanetPhysics/Generalized Fourier Transform
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Fourier-Stieltjes Transform
editGiven 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 .
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editReferences
edit- ↑ 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).