On L1-Approximation

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This monograph discusses the qualitative linear theory of best L1-approximation from finite-dimensional subspaces. It presents a survey of recent research that extends classical results concerned with best-uniform approximation to the more general case. The work is organized to serve as a self-study guide or as a text for advanced courses. It begins with a basic introduction to the concepts of approximation theory before addressing 1- or 2-sided best approximations from finite-dimensional subspaces and approaches to the computation of these. At the end of each chapter is a series of exercises that give the reader an opportunity to test understanding and also contain some theoretical digressions and extensions of the text.
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Editorial Reviews

From the Publisher
"A clearly written, friendly, and enthusiastic introduction to the qualitative theory of best approximation..." American Mathematical Monthly

"...an excellent compendium of the current best known qualitative results on best approximations from finite-dimensional subspaces of L1 spaces....could easily be used in a graduate topics course, and surely will be a standard reference work." Mathematical Reviews

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Product Details

  • ISBN-13: 9780521057691
  • Publisher: Cambridge University Press
  • Publication date: 12/28/2007
  • Series: Cambridge Tracts in Mathematics Series
  • Pages: 252
  • Product dimensions: 5.90 (w) x 8.90 (h) x 0.90 (d)

Table of Contents

Preface; 1. Preliminaries; 2. Approximation from finite-dimensional subspaces of L1; 3. Approximation from finite-dimensional subspaces in C1 (K, ยต); 4. Unicity subspaces and property A; 5. One-sided L1-approximation; 6. Discrete lm1 - approximation; 7. Algorithms; Appendices; References; Author index; Subject index.

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