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Ordered Cones and Approximation

  • Authors
  • Klaus Keimel
  • Walter Roth

Part of the Lecture Notes in Mathematics book series (LNM, volume 1517)

Table of contents

  1. Front Matter
    Pages I-VI
  2. Klaus Keimel, Walter Roth
    Pages 1-7
  3. Klaus Keimel, Walter Roth
    Pages 8-24
  4. Klaus Keimel, Walter Roth
    Pages 25-54
  5. Klaus Keimel, Walter Roth
    Pages 55-67
  6. Klaus Keimel, Walter Roth
    Pages 68-80
  7. Klaus Keimel, Walter Roth
    Pages 81-105
  8. Klaus Keimel, Walter Roth
    Pages 106-128
  9. Back Matter
    Pages 129-134

About this book

Introduction

This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.

Keywords

Locally Convex Cones Ordered Cones Vector space approximation approximation theory boundary element method form function functional functional analysis functions stochastic process stochastic processes theorem

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0089190
  • Copyright Information Springer-Verlag Berlin Heidelberg 1992
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-55445-5
  • Online ISBN 978-3-540-47079-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site