國立虎尾科技大學 |

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

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Ulam's conjecture on invariance of measure in the Hilbert cube/ by Soon-Mo Jung.
Author:	Jung, Soon-Mo.
Published:	Cham :Springer Nature Switzerland : : 2023.,
Description:	x, 190 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
Subject:	Hilbert space. -
Online resource:	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:

580375
Hilbert space.

LC Class. No.: QA322.4

Dewey Class. No.: 515.733

Ulam's conjecture on invariance of measure in the Hilbert cube
LDR:02606nam a2200337 a 4500 001 1106025
003 DE-He213
005 20230628131928.0
006 m d
007 cr nn 008maaau
008 231013s2023 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 785982
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 580375
650 1 4 $a Measure and Integration. $3 672015
650 2 4 $a Functional Analysis. $3 672166
650 2 4 $a Topology. $3 633483
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
830 0 $a Frontiers in mathematics. $3 888364
856 4 0 $u https://doi.org/10.1007/978-3-031-30886-4
950 $a Mathematics and Statistics (SpringerNature-11649)