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Ordered algebraic structures --- Partially ordered sets. --- Schur functions --- Ensembles partiellement ordonnés --- Fonctions de Schur --- Schur functions. --- 51 <082.1> --- Mathematics--Series --- Ensembles partiellement ordonnés --- Partially ordered sets --- S-functions --- Schur's functions --- Holomorphic functions --- Posets --- Sets, Partially ordered --- Ordered sets

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This book is dedicated to Victor Emmanuilovich Katsnelson on the occasion of his 75th birthday and celebrates his broad mathematical interests and contributions.Victor Emmanuilovich’s mathematical career has been based mainly at the Kharkov University and the Weizmann Institute. However, it also included a one-year guest professorship at Leipzig University in 1991, which led to him establishing close research contacts with the Schur analysis group in Leipzig, a collaboration that still continues today. Reflecting these three periods in Victor Emmanuilovich's career, present and former colleagues have contributed to this book with research inspired by him and presentations on their joint work. Contributions include papers in function theory (Favorov-Golinskii, Friedland-Goldman-Yomdin, Kheifets-Yuditskii) , Schur analysis, moment problems and related topics (Boiko-Dubovoy, Dyukarev, Fritzsche-Kirstein-Mädler), extension of linear operators and linear relations (Dijksma-Langer, Hassi-de Snoo, Hassi -Wietsma) and non-commutative analysis (Ball-Bolotnikov, Cho-Jorgensen).

Operator theory. --- Operator Theory. --- Functional analysis --- Schur functions. --- Functional analysis. --- System theory. --- Systems, Theory of --- Systems science --- Science --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- S-functions --- Schur's functions --- Holomorphic functions --- Philosophy

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An Introduction to Quasisymmetric Schur Functions is aimed at researchers and graduate students in algebraic combinatorics. The goal of this monograph is twofold. The first goal is to provide a reference text for the basic theory of Hopf algebras, in particular the Hopf algebras of symmetric, quasisymmetric and noncommutative symmetric functions and connections between them. The second goal is to give a survey of results with respect to an exciting new basis of the Hopf algebra of quasisymmetric functions, whose combinatorics is analogous to that of the renowned Schur functions.

Combinatorial analysis. --- Combinatorics. --- Quasisymmetric groups. --- Schur functions. --- Schur functions --- Quasisymmetric groups --- Combinatorial analysis --- Engineering & Applied Sciences --- Computer Science --- Hopf algebras. --- Combinatorics --- Algebras, Hopf --- S-functions --- Schur's functions --- Mathematics. --- Topological groups. --- Lie groups. --- Applied mathematics. --- Engineering mathematics. --- Algorithms. --- Topological Groups, Lie Groups. --- Applications of Mathematics. --- Algebra --- Mathematical analysis --- Algebraic topology --- Holomorphic functions --- Topological Groups. --- Math --- Science --- Groups, Topological --- Continuous groups --- Algorism --- Arithmetic --- Foundations --- Engineering --- Engineering analysis --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Mathematics

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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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Schur analysis originates with an 1917 article of Schur where he associated to a function, which is analytic and contractive in the open unit disk, a sequence, finite or infinite, of numbers in the open unit disk, called Schur coefficients. In signal processing, they are often named reflection coefficients. Under the word "Schur analysis" one encounters a variety of problems related to Schur functions, such as interpolation problems, moment problems, the study of the relationships between the Schur coefficients and the properties of the function, or the study of underlying operators. Such questions are also considered for some generalizations of Schur functions. Furthermore, there is an extension of the notion of a Schur function for functions that are analytic and have a positive real part in the open upper half-plane; these functions are called Carathéodory functions. This volume is almost entirely dedicated to the analysis of Schur and Carathéodory functions and to the solutions of problems for these classes.

Inverse problems (Differential equations) --- Linear operators. --- Toeplitz operators. --- Hankel operators. --- Wiener-Hopf operators. --- Interpolation. --- Schur functions. --- Moment problems (Mathematics) --- Calculus, Operational --- S-functions --- Schur's functions --- Holomorphic functions --- Approximation theory --- Numerical analysis --- Operators, Wiener-Hopf --- Factorization of operators --- Linear operators --- Operators, Hankel --- Integral operators --- Operators, Toeplitz --- Linear maps --- Maps, Linear --- Operators, Linear --- Operator theory --- Differential equations --- Operator theory. --- System theory. --- Functional analysis. --- Operator Theory. --- Systems Theory, Control. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Functional analysis --- Systems, Theory of --- Systems science --- Science --- Philosophy --- Systems theory.