\({\mathcal L}\)-splines and widths (Q793253)

In this paper the author proves the generalized Bernstein's inequality for the subspace of 2\(\pi\)-periodic \({\mathcal L}\)-splines in the space of 2\(\pi\)-periodic functions with the norm \(_{x}\sup | f(x)|\). Using the theorem of V. M. Tikhomorov concerning the Kolmogorov diameter of a set in a Banach space, the author gives further an estimation of the (2m-1)-dimensional Kolmogorov diameter of an appropriate set in the considered function space.