Embeddings and Extensions in Analysis

  • J. H. Wells
  • L. R. Williams

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete Band 84 book series (MATHE2, volume 84)

Table of contents

  1. Front Matter
    Pages i-vii
  2. J. H. Wells, L. R. Williams
    Pages 1-24
  3. J. H. Wells, L. R. Williams
    Pages 25-45
  4. J. H. Wells, L. R. Williams
    Pages 46-75
  5. J. H. Wells, L. R. Williams
    Pages 76-92
  6. Back Matter
    Pages 102-110

About this book

Introduction

The object of this book is a presentation of the major results relating to two geometrically inspired problems in analysis. One is that of determining which metric spaces can be isometrically embedded in a Hilbert space or, more generally, P in an L space; the other asks for conditions on a pair of metric spaces which will ensure that every contraction or every Lipschitz-Holder map from a subset of X into Y is extendable to a map of the same type from X into Y. The initial work on isometric embedding was begun by K. Menger [1928] with his metric investigations of Euclidean geometries and continued, in its analytical formulation, by I. J. Schoenberg [1935] in a series of papers of classical elegance. The problem of extending Lipschitz-Holder and contraction maps was first treated by E. J. McShane and M. D. Kirszbraun [1934]. Following a period of relative inactivity, attention was again drawn to these two problems by G. Minty's work on non-linear monotone operators in Hilbert space [1962]; by S. Schonbeck's fundamental work in characterizing those pairs (X,Y) of Banach spaces for which extension of contractions is always possible [1966]; and by the generalization of many of Schoenberg's embedding theorems to the P setting of L spaces by Bretagnolle, Dachuna Castelle and Krivine [1966].

Keywords

Analysis Einbettung Erweiterung Extensions Hilbert space Mint banach spaces boundary element method character embedded form metric space object presentation theorem

Authors and affiliations

  • J. H. Wells
    • 1
  • L. R. Williams
    • 2
  1. 1.University of KentuckyLexingtonUSA
  2. 2.Louisiana State UniversityBaton RougeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-66037-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 1975
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-66039-9
  • Online ISBN 978-3-642-66037-5
  • Series Print ISSN 0071-1136
  • About this book