Application of box splines to the approximation of Sobolev spaces (Q921316)

The aim of the paper, as stated by the author, is the construction of approximations of the Sobolev spaces \(W^ m_ p({\mathbb{R}}^ s)\) by certain spaces of discrete functions. The constructions are closely analogous to the finite element approximation of the spaces \(H^ m({\mathbb{R}}^ s)\) presented by \textit{J. P. Aubin} in ``Approximation of Elliptic Boundary - Value Problems'' (1972; Zbl 0248.65063). Work of \textit{T. Reginska} [RAIRO Anal. Numer. 18, 161-174 (1984; Zbl 0554.65043)] is also invoked in the discussion of an application of the approximation to a differential eigenvalue problem in the space \(H^ 1_ 0([0,1])^ 2)\).