Analytic representation for a product of a real analytic and an $L^1$-function in $\Bbb R^n$

Vasko Reckoski

We give an elementary proof of the known result that $P(z)\hat{f}(z)$ is an analytic representation for $f(x)P(x)$, where $P$ is real analytic and $f\in L^1(\Bbb R^n)$ and $\hat f$ is the analytic representation of $f$.