Introduction to modern analysis
著者
書誌事項
Introduction to modern analysis
（Oxford graduate texts in mathematics, 8）
Oxford University Press, 2006, c2003
- : pbk
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注記
Includes bibliographical references and index
"First published 2003. First published in paperback 2006"--T.p. verso
内容説明・目次
内容説明
This new-in-paperback text is based on lectures given by the author at the advanced undergraduate and graduate levels in Measure Theory, Functional Analysis, Banach Algebras, Spectral Theory (of bounded and unbounded operators), Semigroups of Operators, Probability and Mathematical Statistics, and Partial Differential Equations. The first 10 chapters discuss theoretical methods in Measure Theory and Functional Analysis, and contain over 120 end of chapter
exercises. The final two chapters discuss applications in Probability Theory and Partial Differential Equations.
Solutions to the end of chapter exercises may be found on the companion website for this text.
目次
- Preface
- 1. Measures
- 2. Construction of measures
- 3. Measure and topology
- 4. Continuous linear functionals
- 5. Duality
- 6. Bounded operators
- 7. Banach algebras
- 8. Hilbert spaces
- 9. Integral representation
- 10. Unbounded operators
- Application I:Probability
- Application II: Distributions
- Bibliography
- Index
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