Inner product spaces and Fourier Series Approximation

Abstract

The aim of this paper is to give the basic notions of the theory of Fourier Series in connection with Inner production spaces. The preliminary concepts and fundamentals of normed spaces, inner product spaces and the Fourier series are being discussed. The space of all periodic complex integrable functions forms an inner product space. Basic trigonometric functions Sin x and Cos x will form a basis for this linear space. A special emphasis is given in deriving the formulae for the Fourier coefficients. The convergence properties of Fourier series are also studied.