I have to proof the following:

If

Riemann integrable and

continuous, then:

Where a Fourier coefficient

is given by

A hint is given to first proof it for

a trigonometric function and then in general for continuous functions.

What might help in solving this is a property of convolutions. Given two

-periodic Riemann integrable functions

and

on

, then their convolution

on

is defined by

Our property of (probable) interest is: suppose

and

are

-periodic Riemann integrable functions. Then:

.

I'm rather clueless on how to prove this one.. (Worried)