THE RESEARCH PROGRESS OF BNU GROUP ON RELATIVE WIDTHS

Abstract

In this paper, we consider the relative n-widths of two kinds of periodic convolution classes, [Formula: see text] and [Formula: see text], whose convolution kernels K and G are NCVD-kernel and B-kernel. The asymptotic estimations of [Formula: see text] and [Formula: see text] are obtained for p = 1 and ∞, 1 ≤ q ≤ ∞. We also defined a new concept of the average relative widths and obtained the exact results of the average relative widths of the classes of some smooth functions in L2(Rd).