LEADER 04935nam 22006975 450 001 9910254307003321 005 20251113203136.0 010 $a3-319-64546-3 024 7 $a10.1007/978-3-319-64546-9 035 $a(CKB)4340000000223306 035 $a(DE-He213)978-3-319-64546-9 035 $a(MiAaPQ)EBC6312613 035 $a(MiAaPQ)EBC5577009 035 $a(Au-PeEL)EBL5577009 035 $a(OCoLC)1012401036 035 $a(PPN)221247459 035 $a(EXLCZ)994340000000223306 100 $a20171109d2017 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Moment Problem /$fby Konrad Schmüdgen 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XXIII, 512 p. 6 illus.) 225 1 $aGraduate Texts in Mathematics,$x2197-5612 ;$v277 311 08$a3-319-64545-5 320 $aIncludes bibliographical references and index. 327 $aPreface 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. 330 $aThis advanced textbook provides a comprehensive and unified account of the moment problem. It covers the classical one-dimensional theory and its multidimensional generalization, including modern methods and recent developments. In both the one-dimensional and multidimensional cases, the full and truncated moment problems are carefully treated separately. Fundamental concepts, results and methods are developed in detail and accompanied by numerous examples and exercises. Particular attention is given to powerful modern techniques such as real algebraic geometry and Hilbert space operators. A wide range of important aspects are covered, including the Nevanlinna parametrization for indeterminate moment problems, canonical and principal measures for truncated moment problems, the interplay between Positivstellensätze and moment problems on semi-algebraic sets, the fibre theorem, multidimensional determinacy theory, operator-theoretic approaches, and the existence theory and important special topics of multidimensional truncated moment problems. The Moment Problem will be particularly useful to graduate students and researchers working on moment problems, functional analysis, complex analysis, harmonic analysis, real algebraic geometry, polynomial optimization, or systems theory. With notes providing useful background information and exercises of varying difficulty illustrating the theory, this book will also serve as a reference on the subject and can be used for self-study. 410 0$aGraduate Texts in Mathematics,$x2197-5612 ;$v277 606 $aFunctional analysis 606 $aOperator theory 606 $aAlgebraic fields 606 $aPolynomials 606 $aGeometry, Algebraic 606 $aFunctional Analysis 606 $aOperator Theory 606 $aField Theory and Polynomials 606 $aAlgebraic Geometry 615 0$aFunctional analysis. 615 0$aOperator theory. 615 0$aAlgebraic fields. 615 0$aPolynomials. 615 0$aGeometry, Algebraic. 615 14$aFunctional Analysis. 615 24$aOperator Theory. 615 24$aField Theory and Polynomials. 615 24$aAlgebraic Geometry. 676 $a515.72 686 $a44$2MSC 700 $aSchmüdgen$b Konrad$4aut$4http://id.loc.gov/vocabulary/relators/aut$058474 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254307003321 996 $aMoment Problem$91562483 997 $aUNINA