Help need.

Consider the vector space of limited complex series of the uniform norm.

Prove that the Fouriercoefficient c(f) given by the inner product space (from -phi to phi) of the complex conjugate of two functions (f(x)*g(x), where f(x) just is a function and that g(x) in the conjugate), defines a norm reducing function and conclude from this that this function is continuers.

Hint : use either the Bessel or the Cauchy-Schwarz inequality.