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Fourier analysis on wiener measure space

✍ Scribed by Nasiruddin Ahmed

Publisher: Elsevier Science
Year: 1968
Tongue: English
Weight: 356 KB
Volume: 286
Category: Article
ISSN: 0016-0032
DOI: 10.1016/0016-0032(68)90376-1

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✦ Synopsis

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, for nonlinear time invariant systems on the Wiener measure space (fl, Br, ~).

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 Riesg-Fischer theorem which correspond directly to th¢ modified Wienvr's Orthogonal Set (9) are bdieved to be a contribution of this paper.

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