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Functional Analysis, Spectral Theory, and Applications

  • Manfred Einsiedler
  • Thomas Ward

Part of the Graduate Texts in Mathematics book series (GTM, volume 276)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Manfred Einsiedler, Thomas Ward
    Pages 1-14
  3. Manfred Einsiedler, Thomas Ward
    Pages 15-70
  4. Manfred Einsiedler, Thomas Ward
    Pages 71-120
  5. Manfred Einsiedler, Thomas Ward
    Pages 121-133
  6. Manfred Einsiedler, Thomas Ward
    Pages 135-166
  7. Manfred Einsiedler, Thomas Ward
    Pages 167-208
  8. Manfred Einsiedler, Thomas Ward
    Pages 209-252
  9. Manfred Einsiedler, Thomas Ward
    Pages 253-312
  10. Manfred Einsiedler, Thomas Ward
    Pages 313-352
  11. Manfred Einsiedler, Thomas Ward
    Pages 353-408
  12. Manfred Einsiedler, Thomas Ward
    Pages 409-431
  13. Manfred Einsiedler, Thomas Ward
    Pages 433-485
  14. Manfred Einsiedler, Thomas Ward
    Pages 487-502
  15. Manfred Einsiedler, Thomas Ward
    Pages 503-536
  16. Back Matter
    Pages 537-614

About this book

Introduction

This textbook provides a careful treatment of functional analysis and some of its applications in analysis, number theory, and ergodic theory.

In addition to discussing core material in functional analysis, the authors cover more recent and advanced topics, including Weyl’s law for eigenfunctions of the Laplace operator, amenability and property (T), the measurable functional calculus, spectral theory for unbounded operators, and an account of Tao’s approach to the prime number theorem using Banach algebras. The book further contains numerous examples and exercises, making it suitable for both lecture courses and self-study.

Functional Analysis, Spectral Theory, and Applications is aimed at postgraduate and advanced undergraduate students with some background in analysis and algebra, but will also appeal to everyone with an interest in seeing how functional analysis can be applied to other parts of mathematics.

Keywords

functional analysis spectral theory of Banach algebras Pontryagin duality amenable groups property (T) expander graph elliptic regularity Laplace operator prime number theorem measurable functional calculus MSC 46-01, 47-01, 11N05, 20F69, 22B05, 35J25, 35P10, 35P20

Authors and affiliations

  • Manfred Einsiedler
    • 1
  • Thomas Ward
    • 2
  1. 1.ETH ZürichZürichSwitzerland
  2. 2.School of MathematicsUniversity of Leeds LeedsUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-58540-6
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-58539-0
  • Online ISBN 978-3-319-58540-6
  • Series Print ISSN 0072-5285
  • Series Online ISSN 2197-5612
  • Buy this book on publisher's site