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Functional Analysis, Spectral Theory, and Applications

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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 Tao’s 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.

Author(s): Manfred Einsiedler, Thomas Ward
Series: Graduate Texts in Mathematics 276
Edition: 1
Publisher: Springer
Year: 2017

Language: English
Pages: 626

Front Matter ....Pages i-xiv
Motivation (Manfred Einsiedler, Thomas Ward)....Pages 1-14
Norms and Banach Spaces (Manfred Einsiedler, Thomas Ward)....Pages 15-70
Hilbert Spaces, Fourier Series, and Unitary Representations (Manfred Einsiedler, Thomas Ward)....Pages 71-120
Uniform Boundedness and the Open Mapping Theorem (Manfred Einsiedler, Thomas Ward)....Pages 121-133
Sobolev Spaces and Dirichlet’s Boundary Problem (Manfred Einsiedler, Thomas Ward)....Pages 135-166
Compact Self-Adjoint Operators and Laplace Eigenfunctions (Manfred Einsiedler, Thomas Ward)....Pages 167-208
Dual Spaces (Manfred Einsiedler, Thomas Ward)....Pages 209-252
Locally Convex Vector Spaces (Manfred Einsiedler, Thomas Ward)....Pages 253-312
Unitary Operators and Flows, Fourier Transform (Manfred Einsiedler, Thomas Ward)....Pages 313-352
Locally Compact Groups, Amenability, Property (T) (Manfred Einsiedler, Thomas Ward)....Pages 353-408
Banach Algebras and the Spectrum (Manfred Einsiedler, Thomas Ward)....Pages 409-431
Spectral Theory and Functional Calculus (Manfred Einsiedler, Thomas Ward)....Pages 433-485
Self-Adjoint and Symmetric Operators (Manfred Einsiedler, Thomas Ward)....Pages 487-502
The Prime Number Theorem (Manfred Einsiedler, Thomas Ward)....Pages 503-536
Back Matter ....Pages 537-614