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派博传思国际中心 »期刊书目

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Titlebook: Embeddings and Extensions in Analysis; J. H. Wells,L. R. Williams Book 1975 Springer-Verlag Berlin Heidelberg 1975 Analysis.Einbettung.Erw

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书目名称Embeddings and Extensions in Analysis
编辑J. H. Wells,L. R. Williams
视频video
丛书名称Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge
图书封面Titlebook: Embeddings and Extensions in Analysis; J. H. Wells,L. R. Williams Book 1975 Springer-Verlag Berlin Heidelberg 1975 Analysis.Einbettung.Erw
描述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 Schoenbe
出版日期Book 1975
关键词Analysis; Einbettung; Erweiterung; Extensions; Hilbert space; Mint; banach spaces; boundary element method;
版次1
doihttps://doi.org/10.1007/978-3-642-66037-5
isbn_softcover978-3-642-66039-9
isbn_ebook978-3-642-66037-5
copyrightSpringer-Verlag Berlin Heidelberg 1975
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The Classes N(X) and RPD(X) : Integral Representations,s introduced by Schoenberg [79,80,81] and recently refined by Bretagnolle, Dacunha Castelle, and Krivine [11], and Kuelbs [52], we are going to present characterizations of the classes RPD(.) and .(.) when . is one of the spaces ℝ. or . (. = 1,2, … ; 0 < . ≤ ∞ ).
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,The Extension Problem for Lipschitz-Hölder Maps between , Spaces, In this chapter we treat the natural and interesting generalization of this result to . spaces. Starting with two σ-finite measure spaces (Ω, μ) and (.) and initial values for . and . in [1, ∞], the problem is to determine those values of α for which the pair (.(μ), .(.)) has the extension property
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Kandikere R. Sridhar,Namera C. Karunbedded in a given Banach space. First, we consider the question of which metric spaces (.) can be isometrically embedded in a Hilbert space ., that is, under what metric conditions does there exist a map ϕ: . → . such that $$|phi(s)-phi(t)|= ho(s,t)$$ (1.1) for all points . and . in .? Secondly, we
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Anita Kumari,Jyoti Upadhyay,Rohit Joshire natural relatives of inequality (4.15) and the now standard inequalities of Clarkson. These inequalities are crucial to the problem of extending Lipschitz-Hölder maps of order a between . spaces (see §19). In addition they are of considerable intrinsic interest, a point we here emphasize by apply
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