Functional Analysis
An Introduction
Seiten
2004
American Mathematical Society (Verlag)
978-0-8218-3646-0 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-3646-0 (ISBN)
Introduces the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators and spectral theory of self-adjoint operators. This work presents the theorems and methods of abstract functional analysis and applications of these methods to Banach algebras and theory of unbounded self-adjoint operators.
This textbook provides an introduction to the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators, and spectral theory of self-adjoint operators. It also presents the basic theorems and methods of abstract functional analysis and a few applications of these methods to Banach algebras and the theory of unbounded self-adjoint operators. The text corresponds to material for two semester courses (Part I and Part II, respectively) and is essentially self-contained. Prerequisites for the first part are minimal amounts of linear algebra and calculus. For the second part, some knowledge of topology and measure theory is recommended. Each of the 11 chapters is followed by numerous exercises, with solutions given at the end of the book. The amount of mathematics presented in the book can well be absorbed in a year's study and will provide a sound basis for future reading. It is suitable for graduate students and researchers interested in operator theory and functional analysis.
This textbook provides an introduction to the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators, and spectral theory of self-adjoint operators. It also presents the basic theorems and methods of abstract functional analysis and a few applications of these methods to Banach algebras and the theory of unbounded self-adjoint operators. The text corresponds to material for two semester courses (Part I and Part II, respectively) and is essentially self-contained. Prerequisites for the first part are minimal amounts of linear algebra and calculus. For the second part, some knowledge of topology and measure theory is recommended. Each of the 11 chapters is followed by numerous exercises, with solutions given at the end of the book. The amount of mathematics presented in the book can well be absorbed in a year's study and will provide a sound basis for future reading. It is suitable for graduate students and researchers interested in operator theory and functional analysis.
Hilbert spaces and basic operator theory: Linear spaces; normed spaces; first examples Hilbert spaces The dual space Bounded linear operators Spectrum. Fredholm theory of compact operators Self-adjoint operators Functions of operators; spectral decomposition Basics of functional analysis: Spectral theory of unitary operators The fundamental theorems and the basic methods Banach algebras Unbounded self-adjoint and symmetric operators in $H$ Solutions to exercises Bibliography Symbols index Subject index.
| Erscheint lt. Verlag | 1.3.2005 |
|---|---|
| Reihe/Serie | Graduate Studies in Mathematics |
| Zusatzinfo | Illustrations |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 753 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 0-8218-3646-3 / 0821836463 |
| ISBN-13 | 978-0-8218-3646-0 / 9780821836460 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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