Functional analysis, spectral theory, and applications / Manfred Einsiedler, Thomas Ward.

Format:

Book

Author/Creator:

Einsiedler, Manfred Leopold, 1973- author.

Ward, Thomas, 1963- author.

Series:

Graduate texts in mathematics ; 276.

Graduate texts in mathematics, 0072-5285 ; 276

Language:

English

Subjects (All):

Functional analysis.

Spectral theory (Mathematics).

Physical Description:

xiv, 614 pages : illustrations ; 25 cm.

Place of Publication:

Cham, Switzerland : Springer, [2017]

Summary:

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.-- Provided by publisher.

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.

Notes:

Includes bibliographical references and index.

ISBN:

9783319585390

3319585398

OCLC:

982651843