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BANACH-HILBERT SPACES, VECTOR MEASURES AND GROUP REPRESENTATIONS
by Tsoy-Wo Ma (University of Western Australia)
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 measure theory on finite-dimensional Euclidean spaces. This book is ideal for beginners who want to get through the basic material as soon as possible and then do their own research immediately.
Contents:
- Metric Spaces
- Complete, Compact and Connected Sets
- Banach Spaces
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Simplicial Complexes
- Topological Fixed Points
- Foundation of Functional Analysis
- Natural Constructions
- Complex Analysis
- Differentiation in Banach Spaces
- Polynomials and Higher Derivatives
- Ordinary Differential Equations
- Compact Linear Operators
- Operators on Hilbert Spaces
- Spectral Properties of Hilbert Spaces
- Tensor Products
- Complex Vector Lattices
- Vector Measures on Semirings
- Extensions of Positive Measures
- Measurable Objects
- Integrals of Upper Functions
- Vector Integrals
- Finite Products of Measures
- Measures on Finite Dimensional Spaces
- Indefinite Integrals
- Differentiation of Measures
- Spectral Measures
- Locally Compact Spaces
- Almost Periodic Functions on Groups
- Group Representations
- Saturated Closed Invariant Ideals
- Mean Spaces
Readership: Upper level undergraduates, graduate students, academics and
researchers in the field of analysis.
"... a very good introduction to topics in analysis ..."
"... this book is an original and interesting textbook in advanced analysis. Undoubtedly, many students and lecturers will consider the book an accessible and useful introduction to the areas mentioned above."
| 620pp |
Pub. date: Jun 2002 |
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