Sergei Aleksandrovich Telyakovskii

Exact values of relative widths of classes of differentialbe functions

AbstractWe study relative widths in the spacesC andL of classes of periodic differentiable functionsWr,r=1,2,…, when in contrast to the Kolmogorov widths it is additionally required that the approximating functions belong to the classMWr with a given majorantM of the norm of the derivative of orderr. It is proved that ifM satisfies the estimate

Sharpening of the estimates for relative widths of classes of differentiable functions

M \geqslant \frac{4}{{\pi ^2 }}{\text{ log min (}}n{\text{,}}r{\text{) + }}O{\text{(1)}}

Norms on L of Periodic Interpolation Splines with Equidistant Nodes

which is uniform inn andr, then the above-mentionedn-dimensional relative widths of classesWr coincide with the corresponding Kolmogorov widths. Simultaneously, we obtain a uniform (in all the parameters) estimate of the Lebesgue constants of the Zygmund normal means of Fourier series, defined by the factors 1−(k/n)r,k≤n.

Approximation by Bernstein polynomials at the points of discontinuity of the derivatives

AbstractWe consider the series

On the norms of Favard Kernels

\sum\nolimits_{k = 1}^\infty {a_k \sin kx}

Точные значения относительных поперечников классов дифференцируемых функций@@@Exact values of relative widths of classes of differentiable functions

and