Let $f$ be absolutely continuous. Prove that $\hat{f}(n)=o\left(\frac{1}{n}\right)$.
Any hint will be appreciated, thanks.
Let $f$ be absolutely continuous. Prove that $\hat{f}(n)=o\left(\frac{1}{n}\right)$.
Any hint will be appreciated, thanks.
Hint:
Absolute continuous means that $f'\in L^1$. What can you say about the decay of $\hat{f'}$?
Try to lift up the information from 1. to find the decay information on $\hat{f}$.