Banach-Hilbert Spaces, Vector Measures and Group Representations (精装)

媒体关注与评论

...a very good introduction to topics in analysis.. -- Mathematical Reviews, 2003...this book is an original and interesting textbook in advanced analysis. -- Mathematics Abstracts

书籍目录

PrefaceIntroductionChapter 1 Metric SpacesChapter 2 Complete,Compact and Connected SetsChapter 3 Banach SpacesChapter 4 Simplicial ComplexesChapter 5 Topological Fixed PointsChapter 6 Foundation of Functional Analysis Chapter 7 Natural ConstructionsChapter 8 Complex AnalysisChapter 9 Differetiation in Banach SpacesChapter 10 Polynomials and Higher DerivativesChapter 11 Ordinary Differdntial EquaitonsChapter 12 Compact Linear OperatorsChapter 13 Operators on Hilbert SpacesChapter 14 Spectral Properties of Hilbert SpacesChapter 15 Tensor ProductsChapter 16 Complex Vector LatticesChapter 17 Vector Measres on SemiringsChapter 18 Extensions of Positive Measures Chapter 19 Measurable ObjectsChapter 20 Integrals of Upper FunctionsChapter 21 Vector Intgrals Chapter 22 Finite Prosucts of MeasuresChapter 23 Measures on Finite Dimensional SpacesChapter 24 Indefinite Integrals Chapter 25 Differentiation of MeasuresChapter 26 Spectral MeasuresChapter 27 Locally Compact SpacesChapter 28 Almost Periodic Functions on GroupsChapter 29 Group RepresentationsChapter 30 Saturated Closde Invariant IdealsChapter 31 Mean SpacesReferencesIndex

作者简介

　　This book provides an elementary introduction to classical analysis on normed spaces, with special attention paid to fixed points, calculus, and ordinary differential equations It contains a full treatment of vector measures on delta rings without assuming any scalar measure theory and hence should fit well into existing courses  The relation between group representations and almost periodic functions is presented The mean values offer an infinite-dimensional analogue of nasure theory on finite-dimensional Euclidean spaces This book is ideal for beginners who want to get through the basic materialas soon as possible and then do their own research immediately.

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