| Embeddings and Extensions in Analysis Softcover Repri Edition Contributor(s): Wells, J. H. (Author), Williams, L. R. (Author) |
|
 |
ISBN: 3642660398 ISBN-13: 9783642660399 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: November 2011 |
| Additional Information |
| BISAC Categories: - Mathematics | Topology - General |
| Dewey: 514.3 |
| Series: Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge |
| Physical Information: 0.26" H x 6.69" W x 9.61" (0.46 lbs) 110 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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] |