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)