Degree of approximation by lacunary interpolators: $(0,\dots,R-2,R)$ interpolation

Abstract

We propose a modified general technique to derive quantitative assertions on lacunary interpolation by algebraic polynomials. The inequalities obtained are consequences of a smoothing approach. An application to various classical cases such as modified and non-modified (0,2) and (0,1,3) interpolations yields improvements of earlier results.