Infinite dimensional widths and optimal recovery of some smooth function classes of \(L_ p(\mathbb{R})\) in metric \(L(\mathbb{R})\) (Q1312930)

A new class \(W_{prs}(P_ r)=\{f\in L_ s(\mathbb{R})\), \(f^{(r-1)}\) is locally absolutely continuous on \(\mathbb{R}\) and \(\| P_ r\Bigl({d\over dt}\Bigr) f\|_{pq}\leq 1\}\), \(1\leq p\), \(q\), \(s\leq\infty\), \(P_ r\Bigl({d\over dt}\Bigr)=\prod^ r_{j=1}\Bigl({d\over dt}- t_ j\Bigr)\), \(t_ j\in\mathbb{R}\), is introduced. For \(W_{pll}\), among others, the exact expressions of the minimal information diameter, the minimal error of optimal recovery and the minimal linear error are given. No proofs.