Functional Analysis, Spectral Theory, and Applications

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

Autorentext

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.

Inhalt
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.