Probability measures, appel polynomials and polynomial approximation

摘要

In this paper we develop an idea of O. V. Viskov concerning approximation of regular functions by polynomials. We prove, generalizing Viskov, that for every probability measure with finite moments there exists a naturally associated sequence of polynomials such that every sufficiently regular function can be approximated by sums of these polynomials. The error formulas are given in terms of the expectation of the convolution of one of these polynomials with a derivative of the function.