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Graduate Texts in Mathematics

Functional Analysis, Spectral Theory, and Applications

Authors: Einsiedler, Manfred, Ward, Thomas

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  • Presents core material in functional analysis alongside several advanced topics
  • Includes over 400 exercises, with essential exercises marked as such
  • Gives a careful introduction to amenability, property (T), and expander graphs
  • Develops relatively advanced material in spectral theory, including a connection of the spectral theory of Banach algebras to the prime number theorem
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eBook 59,49 €
price for Spain (gross)
  • ISBN 978-3-319-58540-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 72,79 €
price for Spain (gross)
  • ISBN 978-3-319-58539-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 72,79 €
price for Spain (gross)
  • ISBN 978-3-319-86423-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

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.

About the authors

Manfred Einsiedler studied mathematics at the University of Vienna and has been a Professor at the ETH Zürich since 2009. He was an invited speaker at the 2008 European Mathematical Congress in Amsterdam and the 2010 International Congress of Mathematicians in Hyderabad. His primary research area is ergodic theory with connections to number theory. In cooperation with Lindenstrauss and Katok, Einsiedler made significant progress towards the Littlewood conjecture.   

Thomas Ward studied mathematics at the University of Warwick and is Deputy Vice-Chancellor for student education at the University of Leeds. He works in ergodic theory and number theory, and has written several monographs, including Heights of Polynomials and Entropy in Algebraic Dynamics with Graham Everest and Ergodic Theory: with a view towards Number Theory with Manfred Einsiedler. 

Reviews

“All chapters end with a very useful list of additional topics and suggestions for further reading. The book also contains an appendix on set theory and topology, another one on measure theory … . The book is carefully written and provides an interesting introduction to functional analysis with a wealth of both classical and more recent applications.” (Michael M. Neumann, Mathematical Reviews, July, 2018)

“This is an attractive new textbook in functional analysis, aimed at … graduate students. … the large amount of material covered in this book … as well its overall readability, makes it useful as a reference as well as a potential graduate textbook. If you like functional analysis, teach it, or use it in your work, this book certainly merits a careful look.” (Mark Hunacek, MAA Reviews, January, 2018).

“The present book is different from the usual textbooks on functional analysis: it does not only cover the basic material, but also a number of advanced topics which cannot be found in many other books on the subject. … The text is suitable for self-study as well as for the preparation of lectures and seminars. … this is a highly recommendable book for students and researchers alike who are interested in functional analysis and its broad applications.” (Jan-David Hardtke, zbMATH 1387.46001, 2018)


Table of contents (14 chapters)

Table of contents (14 chapters)

Buy this book

eBook 59,49 €
price for Spain (gross)
  • ISBN 978-3-319-58540-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 72,79 €
price for Spain (gross)
  • ISBN 978-3-319-58539-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 72,79 €
price for Spain (gross)
  • ISBN 978-3-319-86423-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Functional Analysis, Spectral Theory, and Applications
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
276
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-58540-6
DOI
10.1007/978-3-319-58540-6
Hardcover ISBN
978-3-319-58539-0
Softcover ISBN
978-3-319-86423-5
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XIV, 614
Number of Illustrations
33 b/w illustrations
Topics