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.
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.
“All chapters end with a very useful list of additional topics and
suggestions for further reading. The book also contains an appendix
on set theory and topology, another one on measure theory … . The
book is carefully written and provides an interesting introduction
to functional analysis with a wealth of both classical and more
recent applications.” (Michael M. Neumann, Mathematical Reviews,
July, 2018)
“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)
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