Recent content by Sonifa

How to prove the following: Suppose f is in the Schwartz Space ( smooth function with very fast decay). Its Fourier transform is smooth and has compact support contained in the interval (1/2,-1/2) Show, ∫ (|f(x)|^2) dx = ∑ (|f(n)|^2) (where integral over R and sum up over n for all intergers)

Finally, I got the same solution as yours. But still many thanks!

The function should be $f(x) = 1 + \cos\bigl(2\pi x\bigr)$ and it is defined on the unict circle R/Z

Let f(x)=1+cos 2\pix and let fk=f*...*f (k-times convolution) what is the value of lim fk(1/2) when k tends to infinity Should use something about the Fourier Analysis, Could someone help me how to solve this problem?