國立高雄大學圖資館 |

Language: English

Back

Spectral theorybasic concepts and ap...

Borthwick, David.

Spectral theorybasic concepts and applications /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Spectral theoryby David Borthwick.
Reminder of title:	basic concepts and applications /
Author:	Borthwick, David.
Published:	Cham :Springer International Publishing :2020.
Description:	x, 338 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Spectral theory (Mathematics)
Online resource:	https://doi.org/10.1007/978-3-030-38002-1
ISBN:	9783030380021$q(electronic bk.)

Spectral theorybasic concepts and applications /
Borthwick, David.

Spectral theorybasic concepts and applications /[electronic resource] :by David Borthwick. - Cham :Springer International Publishing :2020. - x, 338 p. :ill., digital ;24 cm. - Graduate texts in mathematics,2840072-5285 ;. - Graduate texts in mathematics ;129..

1. Introduction -- 2. Hilbert Spaces -- 3. Operators -- 4. Spectrum and Resolvent -- 5. The Spectral Theorem -- 6. The Laplacian with Boundary Conditions -- 7. Schrodinger Operators -- 8. Operators on Graphs -- 9. Spectral Theory on Manifolds -- A. Background Material -- References -- Index.

This textbook offers a concise introduction to spectral theory, designed for newcomers to functional analysis. Curating the content carefully, the author builds to a proof of the spectral theorem in the early part of the book. Subsequent chapters illustrate a variety of application areas, exploring key examples in detail. Readers looking to delve further into specialized topics will find ample references to classic and recent literature. Beginning with a brief introduction to functional analysis, the text focuses on unbounded operators and separable Hilbert spaces as the essential tools needed for the subsequent theory. A thorough discussion of the concepts of spectrum and resolvent follows, leading to a complete proof of the spectral theorem for unbounded self-adjoint operators. Applications of spectral theory to differential operators comprise the remaining four chapters. These chapters introduce the Dirichlet Laplacian operator, Schrodinger operators, operators on graphs, and the spectral theory of Riemannian manifolds. Spectral Theory offers a uniquely accessible introduction to ideas that invite further study in any number of different directions. A background in real and complex analysis is assumed; the author presents the requisite tools from functional analysis within the text. This introductory treatment would suit a functional analysis course intended as a pathway to linear PDE theory. Independent later chapters allow for flexibility in selecting applications to suit specific interests within a one-semester course.

ISBN: 9783030380021$q(electronic bk.)

Standard No.: 10.1007/978-3-030-38002-1doiSubjects--Topical Terms:

182365
Spectral theory (Mathematics)

LC Class. No.: QA320 / .B678 2020

Dewey Class. No.: 515.7222

Spectral theorybasic concepts and applications /
LDR:02874nmm a2200337 a 4500 001 572798
003 DE-He213
005 20200805160040.0
006 m d
007 cr nn 008maaau
008 200925s2020 sz s 0 eng d
020 $a 9783030380021$q(electronic bk.)
020 $a 9783030380014$q(paper)
024 7 $a 10.1007/978-3-030-38002-1 $2 doi
035 $a 978-3-030-38002-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QA320 $b .B678 2020
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 515.7222 $2 23
090 $a QA320 $b .B739 2020
100 1 $a Borthwick, David. $3 753661
245 1 0 $a Spectral theory $h [electronic resource] : $b basic concepts and applications / $c by David Borthwick.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a x, 338 p. : $b ill., digital ; $c 24 cm.
490 1 $a Graduate texts in mathematics, $x 0072-5285 ; $v 284
505 0 $a 1. Introduction -- 2. Hilbert Spaces -- 3. Operators -- 4. Spectrum and Resolvent -- 5. The Spectral Theorem -- 6. The Laplacian with Boundary Conditions -- 7. Schrodinger Operators -- 8. Operators on Graphs -- 9. Spectral Theory on Manifolds -- A. Background Material -- References -- Index.
520 $a This textbook offers a concise introduction to spectral theory, designed for newcomers to functional analysis. Curating the content carefully, the author builds to a proof of the spectral theorem in the early part of the book. Subsequent chapters illustrate a variety of application areas, exploring key examples in detail. Readers looking to delve further into specialized topics will find ample references to classic and recent literature. Beginning with a brief introduction to functional analysis, the text focuses on unbounded operators and separable Hilbert spaces as the essential tools needed for the subsequent theory. A thorough discussion of the concepts of spectrum and resolvent follows, leading to a complete proof of the spectral theorem for unbounded self-adjoint operators. Applications of spectral theory to differential operators comprise the remaining four chapters. These chapters introduce the Dirichlet Laplacian operator, Schrodinger operators, operators on graphs, and the spectral theory of Riemannian manifolds. Spectral Theory offers a uniquely accessible introduction to ideas that invite further study in any number of different directions. A background in real and complex analysis is assumed; the author presents the requisite tools from functional analysis within the text. This introductory treatment would suit a functional analysis course intended as a pathway to linear PDE theory. Independent later chapters allow for flexibility in selecting applications to suit specific interests within a one-semester course.
650 0 $a Spectral theory (Mathematics) $3 182365
650 1 4 $a Partial Differential Equations. $3 274075
650 2 4 $a Operator Theory. $3 274795
650 2 4 $a Functional Analysis. $3 274845
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 https://doi.org/10.1007/978-3-030-38002-1
950 $a Mathematics and Statistics (Springer-11649)