Constructive Approximation: Advanced Problems (Grundlehren der mathematischen Wissenschaften) 1st Edition by George G. Lorentz (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Poor quality paper & font. (I don’t discuss here the content of this book.)

⭐This book has material that is hard to find elsewhere. I came across it looking for a proof of Bernstein’s inequality with a sharp constant. Bernstein’s inequality for trigonometric polynomials is commonly proved in textbooks on harmonic analysis, but with a constant that is not sharp (perhaps the author then mentions that the constant can be improved but hardly anyone bothers to do this). Furthermore, DeVore and Lorentz prove Bernstein’s inequality for 0