I. Introduction. A basic problem in approximation theory is to find complete direct and
converse theorems for approximation by polynomials, splines, rational functions, etc. These …

192 is finite. The primary index here is~ which shows that the order of approximation is like n-
~ while the q gives a finer gradation. During the 1960's, much information [BP, B, Bu] was …

We study nonlinear approximation in L p (R d)(0< p<∞, d> 1) from (a) n-term rational
functions, and (b) piecewise polynomials generated by different anisotropic dyadic partitions …

The approximation properties of simplest fractions (sf's), that is, of the logarithmic derivatives
of complex polynomials, have recently become a subject of intensive research. These …

В последнее время активно изучаются аппроксимативные свойства наипростейших
дробей (н. д.), т. е. логарифмических производных комплексных многочленов …

We prove in this paper the existence of a Schauder basis for C [0, 1] consisting of rational
functions of uniformly bounded degrees. This solves an open question of some years …

An approximation scheme is a family of homogeneous subsets (An) of a quasi-Banach
space X, such that A1⊊ A2⊊…⊊ X, An+ An⊂ AK (n), and∪ nAn¯= X. Continuing the line of …

Recently, A. Cohen, RA DeVore, P. Petrushev, and H. Xu investigated nonlinear
approximation in the space BV (R 2). They modified the classical adaptive algorithm to solve …

This article is a survey of some recent developments which concern two multilevel
approximation schemes:(a) Nonlinear n-term approximation from piecewise polynomials …

We study nonlinear n-term approximation from shifts and dilates of smooth and well-
localized functions in BMO on Rd. A sharp Jackson estimate is established in terms of the …