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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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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

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This book deals with the concept of moments, and how they find application in subsurface hydrologic problems-particularly those dealing with solute transport. This book will be very valuable to researchers who are beginning to learn about moment analysis, and will also be of interest to advanced researchers as well. Both temporal and spatial moments are dealt with in some detail for a wide variety of problems. Several examples using experimental data, both from laboratory columns and field experiments, are provided to give the readers a clear idea about the scope of this method. Apart from conventional uses of moments for solute transport problems, this book contains chapters dealing with use of moments in interval computing, vapour phase transport applications, transfer functions to subsurface tile drains, and construction of breakthrough curves from knowledge of moments.

Soils --- Transformations (Mathematics) --- Moment problems (Mathematics) --- Solute movement. --- Calculus, Operational --- Algorithms --- Differential invariants --- Geometry, Differential --- Movement of solutes in soils --- Soil physics --- Hydraulic engineering. --- Differential equations, partial. --- Geography. --- Hydrogeology. --- Hydrology/Water Resources. --- Partial Differential Equations. --- Earth Sciences, general. --- Cosmography --- Earth sciences --- World history --- Partial differential equations --- Engineering, Hydraulic --- Engineering --- Fluid mechanics --- Hydraulics --- Shore protection --- Hydrology. --- Partial differential equations. --- Earth sciences. --- Geosciences --- Environmental sciences --- Physical sciences --- Aquatic sciences --- Hydrography --- Water --- Geohydrology --- Geology --- Hydrology --- Groundwater

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The origins of Schur analysis lie in a 1917 article by Issai Schur in which he constructed a numerical sequence to correspond to a holomorphic contractive function on the unit disk. These sequences are now known as Schur parameter sequences. Schur analysis has grown significantly since its beginnings in the early twentieth century and now encompasses a wide variety of problems related to several classes of holomorphic functions and their matricial generalizations. These problems include interpolation and moment problems as well as Schur parametrization of particular classes of contractive or nonnegative Hermitian block matrices. This book is primarily devoted to topics related to matrix versions of classical interpolation and moment problems. The major themes include Schur analysis of nonnegative Hermitian block Hankel matrices and the construction of Schur-type algorithms. This book also covers a number of recent developments in orthogonal rational matrix functions, matrix-valued Carathéodory functions and maximal weight solutions for particular matricial moment problems on the unit circle.

Differential equations -- Numerical solutions. --- Differential equations. --- Integral equations -- Numerical solutions. --- Interpolation --- Schur functions --- Inverse problems (Differential equations) --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Applied Mathematics --- Calculus --- Interpolation. --- Schur functions. --- Moment problems (Mathematics) --- S-functions --- Schur's functions --- Mathematics. --- Functions of complex variables. --- Integral transforms. --- Operational calculus. --- Operator theory. --- Operator Theory. --- Integral Transforms, Operational Calculus. --- Functions of a Complex Variable. --- Calculus, Operational --- Holomorphic functions --- Approximation theory --- Numerical analysis --- Integral Transforms. --- Complex variables --- Elliptic functions --- Functions of real variables --- Transform calculus --- Integral equations --- Transformations (Mathematics) --- Functional analysis --- Operational calculus --- Differential equations --- Electric circuits