S. N. Bernstein type estimations in the mean on the curves in a complex plane.
Sampling of Band-Limited Vectors.
Sampling of Paley-Wiener Functions on Stratified Groups.
Sets with the Bernstein and generalized Markov properties
It is known that for determining sets Markov’s property is equivalent to Bernstein’s property. We are interested in finding a generalization of this fact for sets which are not determining. In this paper we give examples of sets which are not determining, but have the Bernstein and generalized Markov properties.
Short proofs for the inequalities of Szegö, Markov and Zygmund
Simultaneous approximation by a class of Bernstein-Durrmeyer operators preserving linear functions
We introduce and study a one-parameter class of positive linear operators constituting a link between the well-known operators of S. N. Bernstein and their genuine Bernstein-Durrmeyer variants. Several limiting cases are considered including one relating our operators to mappings investigated earlier by Mache and Zhou. A recursion formula for the moments is proved and estimates for simultaneous approximation of derivatives are given.
Small values of polynomials: Cartan, Pólya and others.
Smoothness of the Green function for a special domain
We consider a compact set K ⊂ ℝ in the form of the union of a sequence of segments. By means of nearly Chebyshev polynomials for K, the modulus of continuity of the Green functions is estimated. Markov’s constants of the corresponding set are evaluated.
Some exact inequalities of Hardy-Littlewood-Pólya type for periodic functions.
Some results concerning best uniform coapproximation.
Some results for modified Bernstein polynomials.
Spline approximation in , p≤ 1
Stečkin inequalities for summability methods.
Strong converse inequality for a spherical operator.