fourier analysis

Hello,

Does anybody please know how to solve this problem

P10.jpg picture by peacefulsoul1 - Photobucket

i added the definition of f hat
f hat definition picture by peacefulsoul1 - Photobucket

thank you so much

Integrate by parts to see that the term by term differentiation of the Fourier series for f is the series for f', use induction and Riemann Lebesgue for the k-th derivative series.

thank you for the advice, let me try doing this now and get back to you in few minutes, and pretty sure ill be stuck somewhere :) please wait for me

i was able to do this the proof for k =2 which is the following :

d.jpg picture by peacefulsoul1 - Photobucket

here is my work :

2.jpg picture by peacefulsoul1 - Photobucket

how do i proceed ? without using "Riemann Lebesgue" because we have not taken it :S

Your method is fine and more elementary than what I was suggesting, now just apply the same procedure k times (there's no reason to stop at two, everything works the same).