Constructive Approximation: Advanced Problems: v. 304 (Die Grundlehren der Mathematischen Wissenschaften) - Tapa dura

In the last 30 years, Approximation Theory has undergone wonderful develop­ ment, with many new theories appearing in this short interval. This book has its origin in the wish to adequately describe this development, in particular, to rewrite the short 1966 book of G. G. Lorentz, "Approximation of Functions." Soon after 1980, R. A. DeVore and Lorentz joined forces for this purpose. The outcome has been their "Constructive Approximation" (1993), volume 303 of this series. References to this book are given as, for example rCA, p.201]. Later, M. v. Golitschek and Y. Makovoz joined Lorentz to produce the present book, as a continuation of the first. Completeness has not been our goal. In some of the theories, our exposition offers a selection of important, representative theorems, some other cases are treated more systematically. As in the first book, we treat only approximation of functions of one real variable. Thus, functions of several variables, complex approximation or interpolation are not treated, although complex variable methods appear often.

This volume, and its predecessor in the series, cover the whole field of approximation of functions of one real variable. The main subject of this volume is approximation by polymonials, rational functions, splines and operators. There are excursions into the related fields of interpolation, complex variable approximation, wavelets, widths and functional analysis. Emphasis is placed on basic results and illustrative examples, rather than on generality or special problems.