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Functional Analysis / Edition 2

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Overview

This classic text is written for graduate courses in functional analysis. This text is used in modern investigations in analysis and applied mathematics. This new edition includes up-to-date presentations of topics as well as more examples and exercises. New topics include Kakutani's fixed point theorem, Lamonosov's invariant subspace theorem, and an ergodic theorem.

This text is part of the Walter Rudin Student Series in Advanced Mathematics.

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Product Details

Table of Contents

Preface.PART ONE: GENERAL THEORY 1. Topological Vector Space 2. Completeness 3. Convexity 4. Duality in Banach Spaces 5. Some Applications PART TWO: DISTRIBUTIONS AND FOURIER TRANSFORMS 6. Test Functions and Distributions 7. Fourier Transforms 8. Applications to Differential Equations 9. Tauberian Theory PART THREE: BANACH ALGEBRAS AND SPECTRAL THEORY 10. Banach Algebras 11. Commutative Banach Algebras 12. Bounded Operators on a Hillbert Space 13. Unbounded Operators Appendix A: Compactness and Continuity Appendix B: Notes and Comments Bibliography List of Special Symbols Index
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  • Anonymous

    Posted April 4, 2003

    Modern analysis.

    'Modern analysis' used to be a popular name for the subject of this lovely book. It is as important as ever, but perhaps less 'modern'. The subject of functional analysis, while fundamental and central in the landscape of mathematics, really started with seminal theorems due to Banach, Hilbert, von Neumann, Herglotz, Hausdorff, Friedrichs, Steinhouse,...and many other of, the perhaps less well known, founding fathers, in Central Europe (at the time), in the period between the two World Wars. In the beginning it generated awe in its ability to provide elegant proofs of classical theorems that otherwise were thought to be both technical and difficult. The beautiful idea that makes it all clear as daylight: Wiener's theorem on absolutely convergent(AC) Fourier series of 1/f if you can divide, and if f has AC Fourier series, is a case in point. The new subject gained from there because of its many sucess stories,--- in proving new theorems, in unifying old ones, in offering a framework for quantum theory, for dynamical systems, and for partial differential equations. And offering a language that facilitates interdisiplinary work in science! The Journal of Functional Analysis, starting in the 1960ties, broadened the subject, reaching almost all branches of science, and finding functional analytic flavor in theories surprisingly far from the original roots of the subject. The topics in Rudin's book are inspired by harmonic analysis. The later part offers one of the most elegant compact treatment of the theory of operators in Hilbert space, I can think of. Its approach to unbounded operators is lovely.

    1 out of 1 people found this review helpful.

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