{"product_id":"embeddings-and-extensions-in-analysis-j-h-wells-9783642660399","title":"Embeddings and Extensions in Analysis","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].\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e J. H. Wells, L. R. Williams\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3642660398\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783642660399\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 11\/11\/2011\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 110\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.46lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.61h x 6.69w x 0.26d","brand":"J. H. Wells","offers":[{"title":"Paperback","offer_id":46311097696511,"sku":"9783642660399","price":54.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_97b58469-c9cb-4ead-b685-688649148d05.jpg?v=1730888108","url":"https:\/\/www.whiterainbookhouse.com\/products\/embeddings-and-extensions-in-analysis-j-h-wells-9783642660399","provider":"WR Book House","version":"1.0","type":"link"}