000			02604cam a22003375i 4500
020			_a9783319585406
082	0	4	_a515.7 _bEIN _cN-2, P-102
100	1		_aEinsiedler, Manfred,
245	1	0	_aFunctional Analysis, Spectral Theory, and Applications _cManfred Einsiedler, Thomas Ward.
250			_a1st ed.
260			_aUK, _bSpringer, _c2017.
300			_aXIV, 614 pages 33 illustrations
490	1		_aGraduate Texts in Mathematics,
505	0		_aMotivation -- 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.
520			_aThis 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.
650		0	_aDifferential equations.
650		0	_aDynamics.
650		0	_aErgodic theory.
650		0	_aFunctional analysis.
650		0	_aHarmonic analysis.
650		0	_aNumber theory.
650		0	_aPartial differential equations.
650	1	4	_aFunctional Analysis.
650	2	4	_aAbstract Harmonic Analysis.
650	2	4	_aDynamical Systems and Ergodic Theory.
650	2	4	_aNumber Theory.
650	2	4	_aOrdinary Differential Equations.
650	2	4	_aPartial Differential Equations.
700	1		_aWard, Thomas,
942			_cBK
999			_c15405 _d15405