東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回上頁

切換: 標籤 | MARC模式 | ISBD

Ulam's conjecture on invariance of m...

Jung, Soon-Mo.

FindBook

Google Book

Amazon

博客來

Ulam's conjecture on invariance of measure in the Hilbert cube

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Ulam's conjecture on invariance of measure in the Hilbert cube/ by Soon-Mo Jung.
作者:	Jung, Soon-Mo.
出版者:	Cham :Springer Nature Switzerland : : 2023.,
面頁冊數:	x, 190 p. :ill., digital ;24 cm.
內容註:	Preface -- 1. Topology -- 2. Hilbert spaces -- 3. Measure theory -- 4. Extension of isometries -- 5. History of Ulam's conjecture -- 6. Ulam's conjecture. - Bibliography -- Index.
Contained By:	Springer Nature eBook
標題:	Hilbert space. -
電子資源:	https://doi.org/10.1007/978-3-031-30886-4
ISBN:	9783031308864

Ulam's conjecture on invariance of measure in the Hilbert cube
Jung, Soon-Mo.

Ulam's conjecture on invariance of measure in the Hilbert cube[electronic resource] /by Soon-Mo Jung. - Cham :Springer Nature Switzerland :2023. - x, 190 p. :ill., digital ;24 cm. - Frontiers in mathematics,1660-8054. - Frontiers in mathematics..

Preface -- 1. Topology -- 2. Hilbert spaces -- 3. Measure theory -- 4. Extension of isometries -- 5. History of Ulam's conjecture -- 6. Ulam's conjecture. - Bibliography -- Index.

This book discusses the process by which Ulam's conjecture is proved, aptly detailing how mathematical problems may be solved by systematically combining interdisciplinary theories. It presents the state-of-the-art of various research topics and methodologies in mathematics, and mathematical analysis by presenting the latest research in emerging research areas, providing motivation for further studies. The book also explores the theory of extending the domain of local isometries by introducing a generalized span. For the reader, working knowledge of topology, linear algebra, and Hilbert space theory, is essential. The basic theories of these fields are gently and logically introduced. The content of each chapter provides the necessary building blocks to understanding the proof of Ulam's conjecture and are summarized as follows: Chapter 1 presents the basic concepts and theorems of general topology. In Chapter 2, essential concepts and theorems in vector space, normed space, Banach space, inner product space, and Hilbert space, are introduced. Chapter 3 gives a presentation on the basics of measure theory. In Chapter 4, the properties of first- and second-order generalized spans are defined, examined, and applied to the study of the extension of isometries. Chapter 5 includes a summary of published literature on Ulam's conjecture; the conjecture is fully proved in Chapter 6.

ISBN: 9783031308864

Standard No.: 10.1007/978-3-031-30886-4doiSubjects--Topical Terms:

558371
Hilbert space.

LC Class. No.: QA322.4

Dewey Class. No.: 515.733

Ulam's conjecture on invariance of measure in the Hilbert cube
LDR:02606nmm a2200337 a 4500 001 2332372
003 DE-He213
005 20230628131928.0
006 m d
007 cr nn 008maaau
008 240402s2023 sz s 0 eng d
020 $a 9783031308864 $q (electronic bk.)
020 $a 9783031308857 $q (paper)
024 7 $a 10.1007/978-3-031-30886-4 $2 doi
035 $a 978-3-031-30886-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA322.4
072 7 $a PBKL $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKL $2 thema
082 0 4 $a 515.733 $2 23
090 $a QA322.4 $b .J95 2023
100 1 $a Jung, Soon-Mo. $3 3662224
245 1 0 $a Ulam's conjecture on invariance of measure in the Hilbert cube $h [electronic resource] / $c by Soon-Mo Jung.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Birkhäuser, $c 2023.
300 $a x, 190 p. : $b ill., digital ; $c 24 cm.
490 1 $a Frontiers in mathematics, $x 1660-8054
505 0 $a Preface -- 1. Topology -- 2. Hilbert spaces -- 3. Measure theory -- 4. Extension of isometries -- 5. History of Ulam's conjecture -- 6. Ulam's conjecture. - Bibliography -- Index.
520 $a This book discusses the process by which Ulam's conjecture is proved, aptly detailing how mathematical problems may be solved by systematically combining interdisciplinary theories. It presents the state-of-the-art of various research topics and methodologies in mathematics, and mathematical analysis by presenting the latest research in emerging research areas, providing motivation for further studies. The book also explores the theory of extending the domain of local isometries by introducing a generalized span. For the reader, working knowledge of topology, linear algebra, and Hilbert space theory, is essential. The basic theories of these fields are gently and logically introduced. The content of each chapter provides the necessary building blocks to understanding the proof of Ulam's conjecture and are summarized as follows: Chapter 1 presents the basic concepts and theorems of general topology. In Chapter 2, essential concepts and theorems in vector space, normed space, Banach space, inner product space, and Hilbert space, are introduced. Chapter 3 gives a presentation on the basics of measure theory. In Chapter 4, the properties of first- and second-order generalized spans are defined, examined, and applied to the study of the extension of isometries. Chapter 5 includes a summary of published literature on Ulam's conjecture; the conjecture is fully proved in Chapter 6.
650 0 $a Hilbert space. $3 558371
650 1 4 $a Measure and Integration. $3 891263
650 2 4 $a Functional Analysis. $3 893943
650 2 4 $a Topology. $3 522026
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Frontiers in mathematics. $3 1535268
856 4 0 $u https://doi.org/10.1007/978-3-031-30886-4
950 $a Mathematics and Statistics (SpringerNature-11649)