Inner Product Space in Fourier Approximation.

Let f be an element and S a subset of a normed linear space x. A basic Problem of approximation theory is to find an element of S, which is as close as possible to f, i.e. seek an element S* of S such that ‖ f - S* ‖ ? ‖f - s ‖ for all S* in S. This work seeks to use the fourier approximation method using the Inner product space to obtain a best approximation of functions. The fourier approximation in calculus is shown to be a special least square approximation. Define an inner product and norm on c [ -π, π] by the equation. f.g =∫ ?(