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convolution of measurable function with analytic function

Let $f$ be a bounded measurable function with support on the unit disk $\mathbb D \subset \mathbb R^2$ and let $g$ be an analytic function on $\mathbb R^2$. Is it true that the convolution $h = f ...
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Convolution and analyticity

Assume $f$ and $g$ are continuous and related to each other as $$ f(x) = \int _{0}^{x-1} \Big ( (x- y)^2 - 1\Big )^{3/2}g(y) \, dy, \qquad x>1. $$ If we happen to know that $f$ is real analytic ...