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© 1975

Embeddings and Extensions in Analysis

Book

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

  1. 1.University of KentuckyLexingtonUSA
  2. 2.Louisiana State UniversityBaton RougeUSA

Bibliographic information

  • Book Title Embeddings and Extensions in Analysis
  • Authors J.H. Wells
    L.R. Williams
  • Series Title Ergebnisse der Mathematik und ihrer Grenzgebiete Band 84
  • 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
  • Hardcover ISBN 978-3-540-07067-2
  • Softcover ISBN 978-3-642-66039-9
  • eBook ISBN 978-3-642-66037-5
  • Series ISSN 0071-1136
  • Edition Number 1
  • Number of Pages VIII, 110
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Topology
  • Buy this book on publisher's site