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Functional analysis, spectral theory, and applications / Manfred Einsiedler, Thomas Ward.

Einsiedler, Manfred Leopold, 1973- author.; Ward, Thomas, 1963- author.
2017
QA320
Available Online
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Title
Functional analysis, spectral theory, and applications / Manfred Einsiedler, Thomas Ward.
Author
Einsiedler, Manfred Leopold, 1973- author.
ISBN
9783319585406 (electronic book)
3319585401 (electronic book)
9783319585390
DOI
https://doi.org/10.1007/978-3-319-58540-6
Published
Cham, Switzerland : Springer, 2017.
Language
English
Description
1 online resource (xiv, 614 pages) : illustrations.
Item Number
10.1007/978-3-319-58540-6 doi
Call Number
QA320
Dewey Decimal Classification
515/.7
Summary
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.-- Provided by publisher.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed December 5, 2017).
Added Author
Ward, Thomas, 1963- author.
Series
Graduate texts in mathematics ; 276.
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Online Access
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Motivation
Norms and Banach Spaces
Hilbert Spaces, Fourier Series, Unitary Representations
Uniform Boundedness and Open Mapping Theorem
Sobolev Spaces and Dirichlet’s Boundary Problem
Compact Self-Adjoint Operators, Laplace Eigenfunctions
Dual Spaces
Locally Convex Vector Spaces
Unitary Operators and Flows, Fourier Transform
Locally Compact Groups, Amenability, Property (T)
Banach Algebras and the Spectrum
Spectral Theory and Functional Calculus
Self-Adjoint and Symmetric Operators
The Prime Number Theorem
Appendix A: Set Theory and Topology
Appendix B: Measure Theory
Hints for Selected Problems
Notes.

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