Embeddings and Extensions in Analysis
Produktnummer:
181dfc5032911944128a2a46208d95b2ca
Autor: | Wells, J.H. Williams, L.R. |
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Themengebiete: | Analysis Einbettung Erweiterung Extensions Hilbert space Mint banach spaces boundary element method character embedded |
Veröffentlichungsdatum: | 11.11.2011 |
EAN: | 9783642660399 |
Sprache: | Englisch |
Seitenzahl: | 110 |
Produktart: | Kartoniert / Broschiert |
Verlag: | Springer Berlin |
Produktinformationen "Embeddings and Extensions in Analysis"
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].

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