國立虎尾科技大學 |

The moment problem

Record Type:	Language materials, printed : Monograph/item
Title/Author:	The moment problem/ by Konrad Schmudgen.
Author:	Schmudgen, Konrad.
Published:	Cham :Springer International Publishing : : 2017.,
Description:	xxiii, 512 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Moment problems (Mathematics) -
Online resource:	http://dx.doi.org/10.1007/978-3-319-64546-9
ISBN:	9783319645469

The moment problem
Schmudgen, Konrad.

The moment problem[electronic resource] /by Konrad Schmudgen. - Cham :Springer International Publishing :2017. - xxiii, 512 p. :ill., digital ;24 cm. - Graduate texts in mathematics,2770072-5285 ;. - Graduate texts in mathematics ;253..

Preface and Overview -- 1 Integral representations of linear functionals -- 2 Moment problems on abelian *-semigroups -- Part I The one dimensional moment problem -- 3 One dimensional moment problems on intervals: existence -- 4 One dimensional moment problems: determinacy -- 5 Orthogonal polynomials and Jacobi operators -- 6 The operator-theoretic approach to the Hamburger moment problem -- 7 The indeterminate Hamburger moment problem -- 8 The operator-theoretic approach to the Stieltjes moment problem -- Part II The one dimensional truncated moment problem -- 9 The one-dimensional truncated Hamburger and Stieltjes moment problems -- 10 The one-dimensional truncated moment problem on a bounded interval -- 11 The moment problem on the unit circle -- Part III The multidimensional moment problem -- 12 The moment problem on compact semi-algebraic sets -- 13 The moment problem on closed semi-algebraic sets: existence -- 14 The multidimensional moment problem: determinacy -- 15 The complex moment problem -- 16 Semidefinite programming and polynomial optimization -- Part IV The multidimensional truncated moment problem -- 17 Multidimensional truncated moment problems: existence criteria -- 18 Multidimensional truncated moment problems: basic concepts and special topics -- 19 The truncated moment problem for homogeneous polynomials.

This advanced textbook provides a comprehensive and unified account of the moment problem. It covers the classical one-dimensional theory and its multidimensional generalization, including modern methods and recent developments. In both the one-dimensional and multidimensional cases, the full and truncated moment problems are carefully treated separately. Fundamental concepts, results and methods are developed in detail and accompanied by numerous examples and exercises. Particular attention is given to powerful modern techniques such as real algebraic geometry and Hilbert space operators. A wide range of important aspects are covered, including the Nevanlinna parametrization for indeterminate moment problems, canonical and principal measures for truncated moment problems, the interplay between Positivstellensatze and moment problems on semi-algebraic sets, the fibre theorem, multidimensional determinacy theory, operator-theoretic approaches, and the existence theory and important special topics of multidimensional truncated moment problems. The Moment Problem will be particularly useful to graduate students and researchers working on moment problems, functional analysis, complex analysis, harmonic analysis, real algebraic geometry, polynomial optimization, or systems theory. With notes providing useful background information and exercises of varying difficulty illustrating the theory, this book will also serve as a reference on the subject and can be used for self-study.

ISBN: 9783319645469

Standard No.: 10.1007/978-3-319-64546-9doiSubjects--Topical Terms:

1149285
Moment problems (Mathematics)

LC Class. No.: QA432

Dewey Class. No.: 515.72

The moment problem
LDR:03817nam a2200325 a 4500 001 922136
003 DE-He213
005 20180522155015.0
006 m d
007 cr nn 008maaau
008 190624s2017 gw s 0 eng d
020 $a 9783319645469 $q (electronic bk.)
020 $a 9783319645452 $q (paper)
024 7 $a 10.1007/978-3-319-64546-9 $2 doi
035 $a 978-3-319-64546-9
040 $a GP $c GP
041 0 $a eng
050 4 $a QA432
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
082 0 4 $a 515.72 $2 23
090 $a QA432 $b .S356 2017
100 1 $a Schmudgen, Konrad. $3 884249
245 1 4 $a The moment problem $h [electronic resource] / $c by Konrad Schmudgen.
260 $a Cham : $c 2017. $b Springer International Publishing : $b Imprint: Springer,
300 $a xxiii, 512 p. : $b ill., digital ; $c 24 cm.
490 1 $a Graduate texts in mathematics, $x 0072-5285 ; $v 277
505 0 $a Preface and Overview -- 1 Integral representations of linear functionals -- 2 Moment problems on abelian *-semigroups -- Part I The one dimensional moment problem -- 3 One dimensional moment problems on intervals: existence -- 4 One dimensional moment problems: determinacy -- 5 Orthogonal polynomials and Jacobi operators -- 6 The operator-theoretic approach to the Hamburger moment problem -- 7 The indeterminate Hamburger moment problem -- 8 The operator-theoretic approach to the Stieltjes moment problem -- Part II The one dimensional truncated moment problem -- 9 The one-dimensional truncated Hamburger and Stieltjes moment problems -- 10 The one-dimensional truncated moment problem on a bounded interval -- 11 The moment problem on the unit circle -- Part III The multidimensional moment problem -- 12 The moment problem on compact semi-algebraic sets -- 13 The moment problem on closed semi-algebraic sets: existence -- 14 The multidimensional moment problem: determinacy -- 15 The complex moment problem -- 16 Semidefinite programming and polynomial optimization -- Part IV The multidimensional truncated moment problem -- 17 Multidimensional truncated moment problems: existence criteria -- 18 Multidimensional truncated moment problems: basic concepts and special topics -- 19 The truncated moment problem for homogeneous polynomials.
520 $a This advanced textbook provides a comprehensive and unified account of the moment problem. It covers the classical one-dimensional theory and its multidimensional generalization, including modern methods and recent developments. In both the one-dimensional and multidimensional cases, the full and truncated moment problems are carefully treated separately. Fundamental concepts, results and methods are developed in detail and accompanied by numerous examples and exercises. Particular attention is given to powerful modern techniques such as real algebraic geometry and Hilbert space operators. A wide range of important aspects are covered, including the Nevanlinna parametrization for indeterminate moment problems, canonical and principal measures for truncated moment problems, the interplay between Positivstellensatze and moment problems on semi-algebraic sets, the fibre theorem, multidimensional determinacy theory, operator-theoretic approaches, and the existence theory and important special topics of multidimensional truncated moment problems. The Moment Problem will be particularly useful to graduate students and researchers working on moment problems, functional analysis, complex analysis, harmonic analysis, real algebraic geometry, polynomial optimization, or systems theory. With notes providing useful background information and exercises of varying difficulty illustrating the theory, this book will also serve as a reference on the subject and can be used for self-study.
650 0 $a Moment problems (Mathematics) $3 1149285
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Functional Analysis. $3 672166
650 2 4 $a Operator Theory. $3 672127
650 2 4 $a Field Theory and Polynomials. $3 672025
650 2 4 $a Algebraic Geometry. $3 670184
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a Graduate texts in mathematics ; $v 253. $3 774333
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-64546-9
950 $a Mathematics and Statistics (Springer-11649)