Functional Analysis
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Functional Analysis

Introduction to Further Topics in Analysis

Elias M. Stein, Rami Shakarchi

  1. 448 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub
No longer available |Learn more

Functional Analysis

Introduction to Further Topics in Analysis

Elias M. Stein, Rami Shakarchi

Book details
Table of contents
Citations

About This Book

This is the fourth and final volume in the Princeton Lectures in Analysis, a series of textbooks that aim to present, in an integrated manner, the core areas of analysis. Beginning with the basic facts of functional analysis, this volume looks at Banach spaces, Lp spaces, and distribution theory, and highlights their roles in harmonic analysis. The authors then use the Baire category theorem to illustrate several points, including the existence of Besicovitch sets. The second half of the book introduces readers to other central topics in analysis, such as probability theory and Brownian motion, which culminates in the solution of Dirichlet's problem. The concluding chapters explore several complex variables and oscillatory integrals in Fourier analysis, and illustrate applications to such diverse areas as nonlinear dispersion equations and the problem of counting lattice points. Throughout the book, the authors focus on key results in each area and stress the organic unity of the subject.

  • A comprehensive and authoritative text that treats some of the main topics of modern analysis
  • A look at basic functional analysis and its applications in harmonic analysis, probability theory, and several complex variables
  • Key results in each area discussed in relation to other areas of mathematics
  • Highlights the organic unity of large areas of analysis traditionally split into subfields
  • Interesting exercises and problems illustrate ideas
  • Clear proofs provided

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Information

Publisher
Princeton University Press
Year
2011
ISBN
9781400840557
Topic
Mathematics
Subtopic
Functional Analysis
Index
Mathematics

Table of contents

  1. Cover
  2. Half title
  3. Title
  4. Copyright
  5. Dedication
  6. Foreword
  7. Contents
  8. Preface
  9. Chapter 1. Lp Spaces and Banach Spaces
  10. Chapter 2. Lp Spaces in Harmonic Analysis
  11. Chapter 3. Distributions: Generalized Functions
  12. Chapter 4. Applications of the Baire Category Theorem
  13. Chapter 5. Rudiments of Probability Theory
  14. Chapter 6. An Introduction to Brownian Motion
  15. Chapter 7. A Glimpse into Several Complex Variables
  16. Chapter 8. Oscillatory Integrals in Fourier Analysis
  17. Notes and References
  18. Bibliography
  19. Symbol Glossary
  20. Index
Citation styles for Functional Analysis

APA 6 Citation

Stein, E., & Shakarchi, R. (2011). Functional Analysis ([edition missing]). Princeton University Press. Retrieved from https://www.perlego.com/book/735315/functional-analysis-pdf (Original work published 2011)

Chicago Citation

Stein, Elias, and Rami Shakarchi. (2011) 2011. Functional Analysis. [Edition unavailable]. Princeton University Press. https://www.perlego.com/book/735315.

Harvard Citation

Stein, E. and Shakarchi, R. (2011) Functional Analysis. [edition missing]. Princeton University Press. Available at: https://www.perlego.com/book/735315/functional-analysis-pdf (Accessed: 25 September 2021).

MLA 7 Citation

Stein, Elias, and Rami Shakarchi. Functional Analysis. [edition missing]. Princeton University Press, 2011. Web. 25 Sept. 2021.