Geodesic
On extension theorems in spaces of infinitely differentiable functions
Sbornik. Mathematics, Tome 46 (1983) no. 3, pp. 375-389 Cet article a éte moissonné depuis la source Math-Net.Ru

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Conditions on a sequence $\{f_\omega(x)\}$ of functions sufficient for there to exist an extension in the space $$ W^\infty\{a_\alpha,p,r\}\equiv\biggl\{u(x)\in C^\infty(G),\quad\rho(u)\equiv\sum_{|\alpha|=0}^\infty a_\alpha\|D^\alpha u\|_r^p <\infty\biggr\} $$ are established in the one-dimensional case $G\equiv(a,b)$ and also in the multidimensional strip $G\equiv\mathbf R^\nu\times[a, b]$. The conditions obtained reduce matters to a study of convergence of numerical series, and in a number of cases are not only sufficient but also necessary. Bibliography: 9 titles. 
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     author = {G. S. Balashova},
     title = {On extension theorems in spaces of infinitely differentiable functions},
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     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_46_3_a3/}
}
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G. S. Balashova. On extension theorems in spaces of infinitely differentiable functions. Sbornik. Mathematics, Tome 46 (1983) no. 3, pp. 375-389. http://geodesic.mathdoc.fr/item/SM_1983_46_3_a3/

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