Functional Analysis, Spectral Theory, and ...

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Beschreibung

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 Taös 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.

Über den Autor

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 [...]opean 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.

Zusammenfassung

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

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2017
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	628
Reihe:	Graduate Texts in Mathematics
Inhalt:	xiv 614 S. 33 s/w Illustr. 614 p. 33 illus.
ISBN-13:	9783319585390
ISBN-10:	3319585398
Sprache:	Englisch
Herstellernummer:	978-3-319-58539-0
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Ward, Thomas Einsiedler, Manfred
Auflage:	1st ed. 2017
Hersteller:	Springer International Publishing Springer International Publishing AG Graduate Texts in Mathematics
Maße:	241 x 160 x 39 mm
Von/Mit:	Thomas Ward (u. a.)
Erscheinungsdatum:	29.11.2017
Gewicht:	1,098 kg

preigu-id: 110685463