Overview
- 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
Part of the book series: Graduate Texts in Mathematics (GTM, volume 276)
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Table of contents (14 chapters)
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
- ordinary differential equations
- partial differential equations
About this book
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.
Reviews
“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)
Authors and Affiliations
About the authors
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.
Bibliographic Information
Book Title: Functional Analysis, Spectral Theory, and Applications
Authors: Manfred Einsiedler, Thomas Ward
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-3-319-58540-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-58539-0Published: 29 November 2017
Softcover ISBN: 978-3-319-86423-5Published: 30 August 2018
eBook ISBN: 978-3-319-58540-6Published: 21 November 2017
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: XIV, 614
Number of Illustrations: 33 b/w illustrations
Topics: Functional Analysis, Ordinary Differential Equations, Partial Differential Equations, Abstract Harmonic Analysis, Number Theory, Dynamical Systems and Ergodic Theory