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 $\hat{f}$.