Fourier analysis on wiener measure space

Abstract The problem of representation of nonlinear systems on abstract spaces by a complete set of orthogonal functions defined on the same space was partly solved by Wiener, et al. (1–4) for nonlinear time invariant systems on the Wiener measure space (ΣI, BI, μ). This paper gives a simplified exposition of certain well-established results of Wiener and others (1, 6, 7, 8) in terms of non-rigorous concepts such as delta functions and white noise process in order to make the theory accessible to those knowing engineering mathematics. Proofs of Bessel's inequality and the Riesz-Fischer theorem which correspond directly to the modified Wiener's Orthogonal Set (9) are believed to be a contribution of this paper.