Embeddings and Extensions in Analysis

Embeddings and Extensions in Analysis
Author :
Publisher : Springer Science & Business Media
Total Pages : 117
Release :
ISBN-10 : 9783642660375
ISBN-13 : 3642660371
Rating : 4/5 (371 Downloads)

Book Synopsis Embeddings and Extensions in Analysis by : J.H. Wells

Download or read book Embeddings and Extensions in Analysis written by J.H. Wells and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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].


Embeddings and Extensions in Analysis Related Books

Embeddings and Extensions in Analysis
Language: en
Pages: 117
Authors: J.H. Wells
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

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 met
Dimensions, Embeddings, and Attractors
Language: en
Pages: 219
Authors: James C. Robinson
Categories: Mathematics
Type: BOOK - Published: 2010-12-16 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

This accessible research monograph investigates how 'finite-dimensional' sets can be embedded into finite-dimensional Euclidean spaces. The first part brings to
Sobolev Spaces on Metric Measure Spaces
Language: en
Pages: 447
Authors: Juha Heinonen
Categories: Mathematics
Type: BOOK - Published: 2015-02-05 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

This coherent treatment from first principles is an ideal introduction for graduate students and a useful reference for experts.
Methods of Geometric Analysis in Extension and Trace Problems
Language: en
Pages: 431
Authors: Alexander Brudnyi
Categories: Mathematics
Type: BOOK - Published: 2011-10-07 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

The book presents a comprehensive exposition of extension results for maps between different geometric objects and of extension-trace results for smooth functio
Embeddings and Extensions in Analysis
Language: en
Pages: 124
Authors: L R Williams
Categories:
Type: BOOK - Published: 1975-12-01 - Publisher:

DOWNLOAD EBOOK