國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Loewner's theorem on monotone matrix...

Simon, Barry.

Loewner's theorem on monotone matrix functions

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Loewner's theorem on monotone matrix functionsby Barry Simon.
作者:	Simon, Barry.
出版者:	Cham :Springer International Publishing :2019.
面頁冊數:	xi, 459 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Monotonic functions.
電子資源:	https://doi.org/10.1007/978-3-030-22422-6
ISBN:	9783030224226$q(electronic bk.)

Loewner's theorem on monotone matrix functions
Simon, Barry.

Loewner's theorem on monotone matrix functions[electronic resource] /by Barry Simon. - Cham :Springer International Publishing :2019. - xi, 459 p. :ill., digital ;24 cm. - Grundlehren der mathematischen wissenschaften,v.3540072-7830 ;. - Grundlehren der mathematischen wissenschaften ;342..

This book provides an in depth discussion of Loewner's theorem on the characterization of matrix monotone functions. The author refers to the book as a 'love poem,' one that highlights a unique mix of algebra and analysis and touches on numerous methods and results. The book details many different topics from analysis, operator theory and algebra, such as divided differences, convexity, positive definiteness, integral representations of function classes, Pick interpolation, rational approximation, orthogonal polynomials, continued fractions, and more. Most applications of Loewner's theorem involve the easy half of the theorem. A great number of interesting techniques in analysis are the bases for a proof of the hard half. Centered on one theorem, eleven proofs are discussed, both for the study of their own approach to the proof and as a starting point for discussing a variety of tools in analysis. Historical background and inclusion of pictures of some of the main figures who have developed the subject, adds another depth of perspective. The presentation is suitable for detailed study, for quick review or reference to the various methods that are presented. The book is also suitable for independent study. The volume will be of interest to research mathematicians, physicists, and graduate students working in matrix theory and approximation, as well as to analysts and mathematical physicists.

ISBN: 9783030224226$q(electronic bk.)

Standard No.: 10.1007/978-3-030-22422-6doiSubjects--Topical Terms:

182547
Monotonic functions.

LC Class. No.: QA331.5 / .S56 2019

Dewey Class. No.: 515.8

Loewner's theorem on monotone matrix functions
LDR:02451nmm a2200325 a 4500 001 587226
003 DE-He213
005 20200630221858.0
006 m d
007 cr nn 008maaau
008 210326s2019 sz s 0 eng d
020 $a 9783030224226$q(electronic bk.)
020 $a 9783030224219$q(paper)
024 7 $a 10.1007/978-3-030-22422-6 $2 doi
035 $a 978-3-030-22422-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA331.5 $b .S56 2019
072 7 $a PBKB $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKB $2 thema
082 0 4 $a 515.8 $2 23
090 $a QA331.5 $b .S594 2019
100 1 $a Simon, Barry. $3 322335
245 1 0 $a Loewner's theorem on monotone matrix functions $h [electronic resource] / $c by Barry Simon.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2019.
300 $a xi, 459 p. : $b ill., digital ; $c 24 cm.
490 1 $a Grundlehren der mathematischen wissenschaften, $x 0072-7830 ; $v v.354
520 $a This book provides an in depth discussion of Loewner's theorem on the characterization of matrix monotone functions. The author refers to the book as a 'love poem,' one that highlights a unique mix of algebra and analysis and touches on numerous methods and results. The book details many different topics from analysis, operator theory and algebra, such as divided differences, convexity, positive definiteness, integral representations of function classes, Pick interpolation, rational approximation, orthogonal polynomials, continued fractions, and more. Most applications of Loewner's theorem involve the easy half of the theorem. A great number of interesting techniques in analysis are the bases for a proof of the hard half. Centered on one theorem, eleven proofs are discussed, both for the study of their own approach to the proof and as a starting point for discussing a variety of tools in analysis. Historical background and inclusion of pictures of some of the main figures who have developed the subject, adds another depth of perspective. The presentation is suitable for detailed study, for quick review or reference to the various methods that are presented. The book is also suitable for independent study. The volume will be of interest to research mathematicians, physicists, and graduate students working in matrix theory and approximation, as well as to analysts and mathematical physicists.
650 0 $a Monotonic functions. $3 182547
650 0 $a Matrices. $3 181876
650 1 4 $a Real Functions. $3 273779
650 2 4 $a Linear and Multilinear Algebras, Matrix Theory. $3 274063
650 2 4 $a Operator Theory. $3 274795
650 2 4 $a Group Theory and Generalizations. $3 274819
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Grundlehren der mathematischen wissenschaften ; $v 342. $3 597051
856 4 0 $u https://doi.org/10.1007/978-3-030-22422-6
950 $a Mathematics and Statistics (SpringerNature-11649)