Advertisement

n-Widths in Approximation Theory

  • Allan Pinkus

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 7)

Table of contents

  1. Front Matter
    Pages I-X
  2. Allan Pinkus
    Pages 1-8
  3. Allan Pinkus
    Pages 9-38
  4. Allan Pinkus
    Pages 39-62
  5. Allan Pinkus
    Pages 63-137
  6. Allan Pinkus
    Pages 138-197
  7. Allan Pinkus
    Pages 198-231
  8. Allan Pinkus
    Pages 248-276
  9. Back Matter
    Pages 277-294

About this book

Introduction

My original introduction to this subject was through conservations, and ultimate­ ly joint work with C. A. Micchelli. I am grateful to him and to Profs. C. de Boor, E. W. Cheney, S. D. Fisher and A. A. Melkman who read various portions of the manuscript and whose suggestions were most helpful. Errors in accuracy and omissions are totally my responsibility. I would like to express my appreciation to the SERC of Great Britain and to the Department of Mathematics of the University of Lancaster for the year spent there during which large portions of the manuscript were written, and also to the European Research Office of the U.S. Army for its financial support of my research endeavors. Thanks are also due to Marion Marks who typed portions of the manuscript. Haifa, 1984 Allan Pinkus Table of Contents 1 Chapter I. Introduction . . . . . . . . Chapter II. Basic Properties of n-Widths . 9 1. Properties of d • • • • • • • • • • 9 n 15 2. Existence of Optimal Subspaces for d • n n 17 3. Properties of d • • • • • • 20 4. Properties of b • • • • • • n 5. Inequalities Between n-Widths 22 n 6. Duality Between d and d • • 27 n 7. n-Widths of Mappings of the Unit Ball 29 8. Some Relationships Between dn(T), dn(T) and bn(T) . 32 37 Notes and References . . . . . . . . . . . . . .

Keywords

Approximation analytic function approximation theory derivative duality eXist integral mapping mathematics matrices responsibility university

Authors and affiliations

  • Allan Pinkus
    • 1
  1. 1.Department of MathematicsTechnion Israel Institute of TechnologyHaifaIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-69894-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1985
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-69896-5
  • Online ISBN 978-3-642-69894-1
  • Series Print ISSN 0071-1136
  • Buy this book on publisher's site