Geodesic
Spaces of network functions
Sbornik. Mathematics, Tome 15 (1971) no. 2, pp. 183-226

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In this paper, difference analogs of Sobolev–Slobodetskii spaces are studied: $H_s(\Omega)$, where $\Omega$ is either the whole space or a halfspace. One obtains difference analogs of imbedding theorems, on traces and on extensions of network functions from a halfspace to the whole space with preservation of class. Bibliography: 19 titles. 
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     author = {L. S. Frank},
     title = {Spaces of network functions},
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L. S. Frank. Spaces of network functions. Sbornik. Mathematics, Tome 15 (1971) no. 2, pp. 183-226. http://geodesic.mathdoc.fr/item/SM_1971_15_2_a2/