Best Linear Approximation Methods for Some Classes of Analytic Functions on the Unit Disk

Considering Banach Hardy spaces and weighted Bergman spaces, we find the sharp values of the Bernstein, Kolmogorov, Gelfand, and linear n-widths for the classes of analytic functions on the unit disk whose moduli of continuity of the rth derivatives averaged with weight are majorized by a given function satisfying some constraints.

     

On the best mean square approximations by entire functions of exponential type in L 2(ℝ) and mean ν-widths of some functional classes

We consider some extremal problems of approximation theory of functions on the whole real axis ? by entire functions of the exponential type. In particular, we find the exact values of the mean ν-widths of classes of functions, defined by the modules of continuity of the mth order ω _m and majorants ψ satisfying the special type of restriction.