Thread: 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).