Geodesic
Fundamental functions vanishing on a~given set and division by functions
Matematičeskie zametki, Tome 21 (1977) no. 5, pp. 677-689.

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The space $\Psi_V$ of fundamental functions (a subspace of S) consisting of functions vanishing together with all their derivatives on a given closed set $V\subset R^n$ is constructed. Multipliers in $\Psi_V$ are described. In the space $\Psi_V$ is easily realized the division of unity by an infinitely differentiable function, “vanishing slowly” for approximation to its zero set, (in particular, by a polynomial). In the case of a cone $V$ in $R^n$, a description of the dual space $\Phi_V$ consisting of the Fourier preimages of functions of $\Psi_V$ is given. The problem of multipliers in $\Phi_V$ is discussed. 
@article{MZM_1977_21_5_a9,
     author = {S. G. Samko},
     title = {Fundamental functions vanishing on a~given set and division by functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {677--689},
     publisher = {mathdoc},
     volume = {21},
     number = {5},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_5_a9/}
}
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S. G. Samko. Fundamental functions vanishing on a~given set and division by functions. Matematičeskie zametki, Tome 21 (1977) no. 5, pp. 677-689. http://geodesic.mathdoc.fr/item/MZM_1977_21_5_a9/