Introduction
Recall that if V is an inner product space and {a1, a2, . . . , an} is an
orthonormal basis, then an element x of V can be written x=Sum(k=1 to infinity)
IP(x,ak)ak. The coefficients IP(x,ak) are called the Fourier Coefficients of x.
(IP(x,ak) stands for the inner product of x and ak.)
We want to see how this relates to "traditional" Fourier series.
Up to Fourier Series