Embeddings and Extensions in Analysis - Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge 84 (Paperback)
  • Embeddings and Extensions in Analysis - Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge 84 (Paperback)
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Embeddings and Extensions in Analysis - Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge 84 (Paperback)

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Paperback 110 Pages / Published: 11/11/2011
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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].

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN: 9783642660399
Number of pages: 110
Weight: 228 g
Dimensions: 244 x 170 x 6 mm
Edition: Softcover reprint of the original 1st ed. 197

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