Best weighted polynomial approximation on the real line; a functional-analytic approach

AbstractThe rate of convergence of best approximation by algebraic polynomials in weighted Lp(R)-spaces is investigated by functional-analytic methods. Jackson- and Bernstein-type results as well as those of Stečkin- and Zamansky-type are given. The smoothness of the functions involved is measured in terms of the so-called main part modulus of continuity due to Ditzian and Totik, and a modified K-functional