Measure, Integration & Real Analysis · Problem 11C.3

Probability Measures — Sheldon Axler

Mathematics — Measure Theory · fourier-transform-eigenfunction

Problem

Suppose

f(x) = 4\pi x^2 e^{-\pi x^2} - e^{-\pi x^2}

for all

x \in \mathbf{R}

. Show that

\hat{f} = -f