Geodesic
Continuous mean periodic extension of functions from an interval
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 496 (2021), pp. 21-25.

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We study the following version of the mean periodic extension problem. (i) Suppose that $T\in\mathscr{E}'(\mathbb{R}^n)$, $n\ge2$, and $E$ is a nonempty closed subset of $\mathbb{R}^n$. What conditions guarantee that, for a function $f\in C(E)$, there is a function $F\in C(\mathbb{R}^n)$ coinciding with $f$ on $E$ such that $f*T=0$ in $\mathbb{R}^n$? (ii) If such an extension F exists, then estimate the growth of F at infinity. We present a solution of this problem for a broad class of distributions $T$ in the case when $e$ is an interval in $\mathbb{R}^n$.
Keywords: convolution equations, mean periodicity, spherical transform, quasi-analyticity. 
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V. V. Volchkov; Vit. V. Volchkov. Continuous mean periodic extension of functions from an interval. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 496 (2021), pp. 21-25. http://geodesic.mathdoc.fr/item/DANMA_2021_496_a3/

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