國立高雄大學圖資館 |

Language: English

Back

Functional analysis, spectral theory...

Einsiedler, Manfred.

Functional analysis, spectral theory, and applications

Record Type:	Electronic resources : Monograph/item
Title/Author:	Functional analysis, spectral theory, and applicationsby Manfred Einsiedler, Thomas Ward.
Author:	Einsiedler, Manfred.
other author:	Ward, Thomas.
Published:	Cham :Springer International Publishing :2017.
Description:	xiv, 614 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Functional analysis.
Online resource:	http://dx.doi.org/10.1007/978-3-319-58540-6
ISBN:	9783319585406$q(electronic bk.)

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 ;129..

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$q(electronic bk.)

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

200585
Functional analysis.

LC Class. No.: QA320

Dewey Class. No.: 515.7

Functional analysis, spectral theory, and applications
LDR:02597nmm a2200325 a 4500 001 525282
003 DE-He213
005 20180523094725.0
006 m d
007 cr nn 008maaau
008 180904s2017 gw s 0 eng d
020 $a 9783319585406$q(electronic bk.)
020 $a 9783319585390$q(paper)
024 7 $a 10.1007/978-3-319-58540-6 $2 doi
035 $a 978-3-319-58540-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA320
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
082 0 4 $a 515.7 $2 23
090 $a QA320 $b .E35 2017
100 1 $a Einsiedler, Manfred. $3 509078
245 1 0 $a Functional analysis, spectral theory, and applications $h [electronic resource] / $c by Manfred Einsiedler, Thomas Ward.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2017.
300 $a xiv, 614 p. : $b ill., digital ; $c 24 cm.
490 1 $a Graduate texts in mathematics, $x 0072-5285 ; $v 276
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.
650 0 $a Functional analysis. $3 200585
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Functional Analysis. $3 274845
650 2 4 $a Ordinary Differential Equations. $3 273778
650 2 4 $a Partial Differential Equations. $3 274075
650 2 4 $a Abstract Harmonic Analysis. $3 274074
650 2 4 $a Number Theory. $3 274059
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 273794
700 1 $a Ward, Thomas. $3 255456
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Graduate texts in mathematics ; $v 129. $3 436082
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-58540-6
950 $a Mathematics and Statistics (Springer-11649)