Constructive Approximation: 303 (Grundlehren der mathematischen Wissenschaften, 303) - Hardcover

DeVore, Ronald A.; Lorentz, George G.

Hardcover

ISBN 10: 3540506276 ISBN 13: 9783540506270

Publisher: Springer, 1993

Synopsis

The present book deals with some basic problems of Approximation Theory: with properties of polynomials and splines, with approximation by poly- mials, splines, linear operators. It also provides the necessary material ab out different function spaces. In some sense, this is a modern version of the corre­ sponding parts of the book of one of us (Lorentz [A-1966]). We have tried to give a complete exposition of the main, basic theorems of the theory, without going into too much detail, treating the most general cases or discussing very special problems. There are essential limitations: this is a book about approximation of functions of one real variable. But Approxima­ tion Theory of functions of several real or of complex variables would require new books. Very little is given on interpolation. But even with these restric­ tions, proofs of some deep and important results, like Korneichuk's theorems about approximation in Lipschitz spaces, could not be included. Another book, with different authors, "Constructive Approximation, Advanced Problems", is in preparation. There is an extensive bibliography, which can be used also as an Author Index: each paper is supplied with references for the page or pages where it has been used.

About this title

Product Description

Offers a connected, unified exposition of Approximation Theory for functions of one real variable. This book describes spaces of functions such as Sobolev, Lipschitz, Besov rearrangement-invariant function spaces and interpolation of operators.

Review

"This is a stimulating book and a mine of useful techniques and results..." Bulletin of the LMS

Edition details

• Publisher: Springer
• Publication date: 1993
• Language: English
• ISBN 10: 3540506276
• ISBN 13: 9783540506270
• Binding: Hardcover
• Number of pages: 462