Functional Analysis, Spectral Theory, and Applications

• Main Authors: Einsiedler, Manfred (Author), Ward, Thomas (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Series: Graduate Texts in Mathematics, 276
• Subjects: Mathematics.; Harmonic analysis.; Dynamics.; Ergodic theory.; Functional analysis.; Differential equations.; Partial differential equations.; Number theory.; Functional Analysis.; Ordinary Differential Equations.; Partial Differential Equations.; Abstract Harmonic Analysis.; Number Theory.; Dynamical Systems and Ergodic Theory.

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...

Table of Contents:

• 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.