Chapter 7.12, Problem 36P

Normalize $f(x)$ in Problem 21; that is find the factor $N$ so that ${\displaystyle {\int }_{-\infty }^{\infty }|}Nf(x){|}^2=1$.

Let $\psi (x)=Nf(x),$ and find $\varphi (p)$ as given in Problem 35. Verify Parseval’s theorem, that is, show that ${\displaystyle {\int }_{-\infty }^{\infty }|}\varphi (p){|}^{2}dp=1.$