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Functional analysis, spectral theory, and applications

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Functional analysis, spectral theory, and applications/ by Manfred Einsiedler, Thomas Ward.
作者:	Einsiedler, Manfred.
其他作者:	Ward, Thomas.
出版者:	Cham :Springer International Publishing : : 2017.,
面頁冊數:	xiv, 614 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Functional analysis. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-58540-6
ISBN:	9783319585406

Functional analysis, spectral theory, and applications
Einsiedler, Manfred.

Functional analysis, spectral theory, and applications[electronic resource] /by Manfred Einsiedler, Thomas Ward. - Cham :Springer International Publishing :2017. - xiv, 614 p. :ill., digital ;24 cm. - Graduate texts in mathematics,2760072-5285 ;. - Graduate texts in mathematics ;253..

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.

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.

ISBN: 9783319585406

Standard No.: 10.1007/978-3-319-58540-6doiSubjects--Topical Terms:

527706
Functional analysis.

LC Class. No.: QA320

Dewey Class. No.: 515.7

Functional analysis, spectral theory, and applications
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505 0 $a 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.
520 $a 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.
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650 2 4 $a Functional Analysis. $3 672166
650 2 4 $a Ordinary Differential Equations. $3 670854
650 2 4 $a Partial Differential Equations. $3 671119
650 2 4 $a Abstract Harmonic Analysis. $3 672075
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650 2 4 $a Dynamical Systems and Ergodic Theory. $3 671353
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