Fourier-Stieltjes series

Fourier-Stieltjes series

[‚fu̇r·ē‚ā ′stēl·yes ‚sir·ēz]
(mathematics)
For a function ƒ(x) of bounded variation on the interval [0,2π], the series from n = 0 to infinity of cn exp (inx), where cn is 1/2π times the integral from x = 0 to x = 2π of exp (-inx) d ƒ(x).
References in periodicals archive ?
P] [0, 2[pi]], P [greater than or equal to] [alpha], the question of the convergence of associated random Fourier-Stieltjes series
2] [0, 2[pi]] and X is the standard Brownian motion process it is not hard to show that the random Fourier-Stieltjes series converge almost surely to the stochastic integral (4), as An are independent.
beta]] with [beta] [member of] (0,1) and a symmetric stable process X of index [alpha] [member of] (1,2) with [alpha][beta] > 1 , the random Fourier-Stieltjes series [[infinity].