Functional Analysis, Spectral Theory, and ...

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Beschreibung

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

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

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:	2018
Fachbereich:	Analysis
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Graduate Texts in Mathematics
Inhalt:	xiv 614 S. 33 s/w Illustr. 614 p. 33 illus.
ISBN-13:	9783319864235
ISBN-10:	3319864238
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Einsiedler, Manfred Ward, Thomas
Auflage:	Softcover reprint of the original 1st edition 2017
Hersteller:	Springer Springer International Publishing AG Graduate Texts in Mathematics
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 34 mm
Von/Mit:	Manfred Einsiedler (u. a.)
Erscheinungsdatum:	30.08.2018
Gewicht:	0,937 kg