Characterizations for the family of functions classes {B^r_p,q,N} and their connection with Besov’s spaces

Abstract

In this paper we define families of classes of functions related to best approximations in harmonic intervals. These families of function classes characterize the order of approximation of functions by trigonometric polynomials with a spectrum from harmonic intervals. The article contains an investigation of various characterizations of the indicated families of function classes, introduces imbedding theorems, and shows the connection between the introduced families of functions classes and the classical Besov spaces. The article is intended for researchers specializing in the theory of approximation and functional analysis, and all those whose interests lie in these areas.