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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 ...
