{"product_id":"embeddings-and-extensions-in-analysis-von-j-h-wells-l-r-williams","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].\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783642660399\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783642660399","offer_id":39431224426589,"sku":"9783642660399","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/c3c7b3f8-9ea3-4435-b232-9db771dbfb6e.jpg?v=1772086869","url":"https:\/\/shop.autorenwelt.de\/products\/embeddings-and-extensions-in-analysis-von-j-h-wells-l-r-williams","provider":"Autorenwelt Shop","version":"1.0","type":"link"}