Uniform Approximation of Functions with Discrete Approximation Functionals

Discrete approximation of functionals with jumps and creases

Let H(0, L) denote the space of piecewise-H functions on the interval (0, L); if u ∈ H(0, L) then u, u′ and u′′ are regarded as defined on the whole interval (0, L), and u and u′ are piecewise-continuous functions. Let S(u) be the set of the discontinuity points (jump points) of the function u ∈ H(0, L) and, with a slight abuse of notation, denote by S(u′) the set of crease points of u (i.e., t...

The best uniform polynomial approximation of two classes of rational functions

In this paper we obtain the explicit form of the best uniform polynomial approximations out of Pn of two classes of rational functions using properties of Chebyshev polynomials. In this way we present some new theorems and lemmas. Some examples will be given to support the results.

Uniform approximation by discrete least squares polynomials

We study uniform approximation of differentiable or analytic functions of one or several variables on a compact set K by a sequence of discrete least squares polynomials. In particular, if K satisfies a Markov inequality and we use point evaluations on standard discretization grids with the number of points growing polynomially in the degree, these polynomials provide nearly optimal approximant...

On Padé Approximation of Some Practical Functions

UNIFORM APPROXIMATION BY b – HARMONIC FUNCTIONS

The Mergelyan and Ahlfors-Beurling estimates for the Cauchy transform give quantitative information on uniform approximation by rational functions with poles off K. We will present an analogous result for an integral transform on the unit sphere in C2 introduced by Henkin, and show how it can be used to study approximation by functions that are locally harmonic with respect to the Kohn Laplacia...