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In this paper, we specify a set of optimal subspaces for $L_2$ approximationof three classes of functions in the Sobolev space $W^{(r)}_2$, defined on asegment and subject to certain boundary conditions. All of these subspaces aregenerated by equidistant shifts of a single function. In particular, weindicate optimal spline spaces of all degrees $d\geqslant r-1$ with uniformknots.

Optimal subspaces for mean square approximation of classes of differentiable functions with boundary conditions