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Moment problems (Mathematics) --- Geometry, Algebraic --- Mathematical optimization

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Algebra --- Moment problems (Mathematics) --- Problèmes des moments (mathématiques) --- Matrices. --- Matrices --- Calculus, Operational --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal

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This volume contains six peer-refereed articles written on the occasion of the workshop "Operator theory, system theory and scattering theory: multidimensional generalizations and related topics", held at the Ben-Gurion University of the Negev from June 26 to July 1, 2005. The contributions which both survey their respective fields and contain new results present a cross-section of current activity in operator theory and system theory. Topics considered include Schur analysis, hierarchical semiseparable matrices, canonical forms for pairs of quaternionic matrices, the theory of homogeneous operators, algebras of fractions of continuous functions, and moment problems. Schur analysis in its various aspects occupies more than half of the volume, and moments problems have also an important place in the papers presented here. The volume will be of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists. .

Operator theory --- Schur functions --- Moment problems (Mathematics) --- Quaternions --- Algebra, Universal --- Algebraic fields --- Curves --- Surfaces --- Numbers, Complex --- Vector analysis --- Calculus, Operational --- S-functions --- Schur's functions --- Holomorphic functions --- Operator theory. --- Global analysis (Mathematics). --- Operator Theory. --- Analysis. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Functional analysis --- Mathematical analysis. --- Analysis (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis

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Operator theory --- Complex analysis --- 51 <082.1> --- Mathematics--Series --- Schur functions --- Interpolation spaces. --- Moment problems (Mathematics) --- Lyapunov functions. --- Schur, Fonctions de --- Espaces d'interpolation --- Problèmes des moments (mathématiques) --- Interpolataion spaces --- Lyapunov functions --- S-functions --- Schur's functions --- Holomorphic functions --- Calculus, Operational --- Functions, Liapunov --- Liapunov functions --- Differential equations --- Schur, Fonctions de. --- Espaces d'interpolation.

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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 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.

Integraltransformer --- Mathematics. --- Algebraic geometry. --- Algebra. --- Field theory (Physics). --- Functional analysis. --- Operator theory. --- Functional Analysis. --- Operator Theory. --- Field Theory and Polynomials. --- Algebraic Geometry. --- Functional calculus --- Classical field theory --- Continuum physics --- Algebraic geometry --- Math --- Geometry, algebraic. --- Functional analysis --- Calculus of variations --- Functional equations --- Integral equations --- Physics --- Continuum mechanics --- Geometry --- Moment problems (Mathematics) --- Mathematics --- Mathematical analysis