Geodesic
On~the extension of infinitely differentiable functions
Izvestiya. Mathematics , Tome 31 (1988) no. 3, pp. 603-620.

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Conditions on logarithmically convex sequences $\{M_n\}$ and $\{\widehat M_n\}$ are obtained under which, for every sequence $\{b_n\}$ with $|b_n|$, $n=0,1,2,\dots$, there exists an infinitely differentiable function $f(x)$ such that $f_{(0)}^{(n)}=b_n$ and $\|f^{(n)}\|_{L_p(R)}\leqslant C_2^n\widehat M_n(p)$, $1\leqslant p\leqslant\infty$. Bibliography: 17 titles. 
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G. S. Balashova. On~the extension of infinitely differentiable functions. Izvestiya. Mathematics , Tome 31 (1988) no. 3, pp. 603-620. http://geodesic.mathdoc.fr/item/IM2_1988_31_3_a7/

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