Measure, Integration & Real Analysis · Problem 11C.20

Probability Measures — Sheldon Axler

Mathematics — Measure Theory · fourier-transform-convolution-L2

Problem

Prove that if

f \in L^1(\mathbf{R})

and

g \in L^2(\mathbf{R})

, then

\mathcal{F}(f * g) = \hat{f} \mathcal{F}g