TOPICS
Search

Fourier-Stieltjes Transform


Let f(x) be a positive definite, measurable function on the interval (-infty,infty). Then there exists a monotone increasing, real-valued bounded function alpha(t) such that

 f(x)=int_(-infty)^inftye^(itx)dalpha(t)

for "almost all" x. If alpha(t) is nondecreasing and bounded and f(x) is defined as above, then f(x) is called the Fourier-Stieltjes transform of alpha(t), and is both continuous and positive definite.


See also

Fourier Transform, Laplace Transform

Explore with Wolfram|Alpha

References

Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 618, 1980.

Referenced on Wolfram|Alpha

Fourier-Stieltjes Transform

Cite this as:

Weisstein, Eric W. "Fourier-Stieltjes Transform." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Fourier-StieltjesTransform.html

Subject classifications