Constructive Approximation (Grundlehren der mathematischen Wissenschaften, 303) 1993rd Edition by Ronald A. DeVore (PDF)

Description

Coupled with its sequel, this book gives a connected, unified exposition of Approximation Theory for functions of one real variable. It describes spaces of functions such as Sobolev, Lipschitz, Besov rearrangement-invariant function spaces and interpolation of operators. Other topics include Weierstrauss and best approximation theorems, properties of polynomials and splines. It contains history and proofs with an emphasis on principal results.

User’s Reviews

Editorial Reviews: Review “This is a stimulating book and a mine of useful techniques and results…” Bulletin of the LMS

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