Chebyshev Ω- Splines and N-Widths of WrHω[0, 1]

TL;DRAbstract

In this chapter we review the Tihomirov’s result that identifies the extremal functional and optimal approximating subspaces in the problem of N-widths of Sobolev classes \( {{W}^{r}}{{H}^{\omega }}[0,1] \). Then, we describe analogs of Chebyshev ω-splines in the problem of N-widths of functional classes W r H ω[0, 1] for nonlinear ω.

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