Overview

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.

Full Product Details

Author:   Ronald A. DeVore ,  George G. Lorentz
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of hardcover 1st ed. 1993
Volume:   303
Dimensions:   Width: 15.50cm , Height: 2.30cm , Length: 23.50cm
Weight:   0.712kg
ISBN:  

9783642080753

ISBN 10:   3642080758
Pages:   452
Publication Date:   01 December 2010
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1. Theorems of Weierstrass.- 2. Spaces of Functions.- 3. Best Approximation.- 4. Properties of Polynomials.- 5. Splines.- 6. K-Functionals and Interpolation Spaces.- 7. Central Theorems of Approximation.- 8. Influence of Endpoints in Polynomial Approximation.- 9. Approximation by Operators.- 10. Bernstein Polynomials.- 11. Approximation of Classes of Functions, Müntz Theorems.- 12. Spline Approximation.- 13. Spline Interpolation and Projections onto Spline Spaces.

Reviews

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

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