Geodesic
Inverse approximation theorem on an infinite union of segments
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 30, Tome 290 (2002), pp. 168-176 
N. A. Shirokov. Inverse approximation theorem on an infinite union of segments. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 30, Tome 290 (2002), pp. 168-176. http://geodesic.mathdoc.fr/item/ZNSL_2002_290_a7/
@article{ZNSL_2002_290_a7,
     author = {N. A. Shirokov},
     title = {Inverse approximation theorem on an infinite union of segments},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {168--176},
     year = {2002},
     volume = {290},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_290_a7/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $E=\bigcup\limits^{\infty}_{n=-\infty}[a_n, b_n]$, where $a_n$ and $b_n$ satisfy $0, $0 $n=0,\pm1,\pm2$. Denote by $B_{\sigma}$ the class of all entire functions of exponential type $\le\sigma$ bounded on the real axis. Under certain assumptions on the rate of approximation on $E$ of a bounded function $f$ by functions in $B_{\sigma}$ ($\sigma$ varies), we get some information about the smoothness of $f$.