Graduate Texts in Mathematics

Functional Analysis, Spectral Theory, and Applications

Authors: Einsiedler, Manfred, Ward, Thomas

  • 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 $69.99
price for USA (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 $89.99
price for USA
  • ISBN 978-3-319-58539-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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.

Table of contents (14 chapters)

  • Motivation

    Einsiedler, Manfred (et al.)

    Pages 1-14

  • Norms and Banach Spaces

    Einsiedler, Manfred (et al.)

    Pages 15-70

  • Hilbert Spaces, Fourier Series, and Unitary Representations

    Einsiedler, Manfred (et al.)

    Pages 71-120

  • Uniform Boundedness and the Open Mapping Theorem

    Einsiedler, Manfred (et al.)

    Pages 121-133

  • Sobolev Spaces and Dirichlet’s Boundary Problem

    Einsiedler, Manfred (et al.)

    Pages 135-166

Buy this book

eBook $69.99
price for USA (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 $89.99
price for USA
  • ISBN 978-3-319-58539-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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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
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XIV, 614
Number of Illustrations and Tables
33 b/w illustrations
Topics