國立虎尾科技大學 |

Spectral and Scattering Theory for Ordinary Differential Equations = Vol. I: Sturm–Liouville Equations /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Spectral and Scattering Theory for Ordinary Differential Equations/ by Christer Bennewitz, Malcolm Brown, Rudi Weikard.
Reminder of title:	Vol. I: Sturm–Liouville Equations /
Author:	Bennewitz, Christer.
other author:	Brown, Malcolm.
Description:	IX, 379 p.online resource. :
Contained By:	Springer Nature eBook
Subject:	Mathematical analysis. -
Online resource:	https://doi.org/10.1007/978-3-030-59088-8
ISBN:	9783030590888

Spectral and Scattering Theory for Ordinary Differential Equations = Vol. I: Sturm–Liouville Equations /
Bennewitz, Christer.

Spectral and Scattering Theory for Ordinary Differential EquationsVol. I: Sturm–Liouville Equations /[electronic resource] :by Christer Bennewitz, Malcolm Brown, Rudi Weikard. - 1st ed. 2020. - IX, 379 p.online resource. - Universitext,0172-5939. - Universitext,.

1 Introduction -- 2 Hilbert space -- 3 Abstract spectral theory -- 4 Sturm–Liouville equations -- 5 Left-definite Sturm–Liouville equations -- 6 Oscillation, spectral asymptotics and special functions -- 7 Uniqueness of the inverse problem -- 8 Scattering -- A Functional analysis -- B Stieltjes integrals -- C Schwartz distributions -- D Ordinary differential equations -- E Analytic functions -- F The Camassa–Holm equation -- References -- Symbol Index -- Subject Index.

This graduate textbook offers an introduction to the spectral theory of ordinary differential equations, focusing on Sturm–Liouville equations. Sturm–Liouville theory has applications in partial differential equations and mathematical physics. Examples include classical PDEs such as the heat and wave equations. Written by leading experts, this book provides a modern, systematic treatment of the theory. The main topics are the spectral theory and eigenfunction expansions for Sturm–Liouville equations, as well as scattering theory and inverse spectral theory. It is the first book offering a complete account of the left-definite theory for Sturm–Liouville equations. The modest prerequisites for this book are basic one-variable real analysis, linear algebra, as well as an introductory course in complex analysis. More advanced background required in some parts of the book is completely covered in the appendices. With exercises in each chapter, the book is suitable for advanced undergraduate and graduate courses, either as an introduction to spectral theory in Hilbert space, or to the spectral theory of ordinary differential equations. Advanced topics such as the left-definite theory and the Camassa–Holm equation, as well as bibliographical notes, make the book a valuable reference for experts.

ISBN: 9783030590888

Standard No.: 10.1007/978-3-030-59088-8doiSubjects--Topical Terms:

527926
Mathematical analysis.

LC Class. No.: QA299.6-433

Dewey Class. No.: 515

Spectral and Scattering Theory for Ordinary Differential Equations = Vol. I: Sturm–Liouville Equations /
LDR:03205nam a22003975i 4500 001 1018984
003 DE-He213
005 20201027122006.0
007 cr nn 008mamaa
008 210318s2020 gw | s |||| 0|eng d
020 $a 9783030590888 $9 978-3-030-59088-8
024 7 $a 10.1007/978-3-030-59088-8 $2 doi
035 $a 978-3-030-59088-8
050 4 $a QA299.6-433
072 7 $a PBK $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBK $2 thema
082 0 4 $a 515 $2 23
100 1 $a Bennewitz, Christer. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1314110
245 1 0 $a Spectral and Scattering Theory for Ordinary Differential Equations $h [electronic resource] : $b Vol. I: Sturm–Liouville Equations / $c by Christer Bennewitz, Malcolm Brown, Rudi Weikard.
250 $a 1st ed. 2020.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a IX, 379 p. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Universitext, $x 0172-5939
505 0 $a 1 Introduction -- 2 Hilbert space -- 3 Abstract spectral theory -- 4 Sturm–Liouville equations -- 5 Left-definite Sturm–Liouville equations -- 6 Oscillation, spectral asymptotics and special functions -- 7 Uniqueness of the inverse problem -- 8 Scattering -- A Functional analysis -- B Stieltjes integrals -- C Schwartz distributions -- D Ordinary differential equations -- E Analytic functions -- F The Camassa–Holm equation -- References -- Symbol Index -- Subject Index.
520 $a This graduate textbook offers an introduction to the spectral theory of ordinary differential equations, focusing on Sturm–Liouville equations. Sturm–Liouville theory has applications in partial differential equations and mathematical physics. Examples include classical PDEs such as the heat and wave equations. Written by leading experts, this book provides a modern, systematic treatment of the theory. The main topics are the spectral theory and eigenfunction expansions for Sturm–Liouville equations, as well as scattering theory and inverse spectral theory. It is the first book offering a complete account of the left-definite theory for Sturm–Liouville equations. The modest prerequisites for this book are basic one-variable real analysis, linear algebra, as well as an introductory course in complex analysis. More advanced background required in some parts of the book is completely covered in the appendices. With exercises in each chapter, the book is suitable for advanced undergraduate and graduate courses, either as an introduction to spectral theory in Hilbert space, or to the spectral theory of ordinary differential equations. Advanced topics such as the left-definite theory and the Camassa–Holm equation, as well as bibliographical notes, make the book a valuable reference for experts.
650 0 $a Mathematical analysis. $3 527926
650 0 $a Analysis (Mathematics). $3 1253570
650 0 $a Operator theory. $3 527910
650 0 $a Special functions. $3 1257411
650 0 $a Mathematical physics. $3 527831
650 1 4 $a Analysis. $3 669490
650 2 4 $a Operator Theory. $3 672127
650 2 4 $a Special Functions. $3 672152
650 2 4 $a Mathematical Physics. $3 786661
700 1 $a Brown, Malcolm. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1314111
700 1 $a Weikard, Rudi. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1314112
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030590871
776 0 8 $i Printed edition: $z 9783030590895
830 0 $a Universitext, $x 0172-5939 $3 1253835
856 4 0 $u https://doi.org/10.1007/978-3-030-59088-8
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)