Geodesic
The infinitely differentiable extension of systems of functions
Matematičeskie zametki, Tome 9 (1971) no. 6, pp. 723-734

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The “best” extension of systems of functions of real variables from an $(n-1)$-dimensional hyperplane $E_{n?1}$ to the whole of $E_n$ is investigated. It is shown that extension can be realized to a function, infinitely differentiable outside $E_{n?1}$, whose derivatives have in a certain sense the best possible rate of growth close to $E_{n?1}$ functions (the $B$-class). 
@article{MZM_1971_9_6_a13,
     author = {O. A. Gavrilova},
     title = {The infinitely differentiable extension of systems of functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {723--734},
     publisher = {mathdoc},
     volume = {9},
     number = {6},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_9_6_a13/}
}
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O. A. Gavrilova. The infinitely differentiable extension of systems of functions. Matematičeskie zametki, Tome 9 (1971) no. 6, pp. 723-734. http://geodesic.mathdoc.fr/item/MZM_1971_9_6_a13/