Approximation By Bandlimited Functions, Generalized K-Functionals and Generalized Moduli of Smoothness

摘要

We study properties of generalized K-functionals and generalized moduli of smoothness in L-p() spaces with 1 p < as well as in the space C() of uniformly continuous and bounded functions. We obtain direct Jackson-type estimates and inverse Bernstein-type estimates. We show the equivalence between approximation error of convolution integrals generated by an arbitrary generator with compact support, generalized K-functionals generated by homogeneous functions and generalized moduli of smoothness. Our approach covers classical approximation methods, K-functionals related to fractional derivatives and fractional moduli of smoothness.