Properties of a family of operators of generalized translation with applications to approximation theory (Q5951058)

If \(f\) is a \(2\pi\)-periodic function, then the degree of approximation by trigonometric polynomials is bounded by a multiple of \(\omega (f, 1/n)\) the modulus of continuity of \(f\). This work proves that the completely analogous statement can be for the degree of approximation of non-periodic functions by algebraic polynomials provided a generalized modulus of continuity is used. The generalization used here is defined using operators of generalized translation. This paper introduces a family of non-symmetric operators of generalized translations, studies its properties and applies them to bound the degree of approximation.