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Operator theory --- Contraction operators --- Factorization of operators --- Hilbert space --- Model theory --- Logic, Symbolic and mathematical --- Banach spaces --- Hyperspace --- Inner product spaces --- Operators, Factorization of --- Factorization (Mathematics) --- Factors (Algebra) --- Wiener-Hopf operators --- Contracting operators --- Operators, Contracting --- Operators, Contraction --- Linear operators --- Contraction operators. --- Factorization of operators. --- Model theory. --- Hilbert space. --- Hilbert, Espaces de. --- Théorie des modèles. --- Factorisation d'opérateurs. --- Opérateurs de contraction. --- Théorie des modèles
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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.
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The present book deals with canonical factorization problems for di?erent classes of matrix and operator functions. Such problems appear in various areas of ma- ematics and its applications. The functions we consider havein common that they appear in the state space form or can be represented in such a form. The main results are all expressed in terms of the matrices or operators appearing in the state space representation. This includes necessary and su?cient conditions for canonical factorizations to exist and explicit formulas for the corresponding f- tors. Also, in the applications the entries in the state space representation play a crucial role. Thetheorydevelopedinthebookisbasedonageometricapproachwhichhas its origins in di?erent ?elds. One of the initial steps can be found in mathematical systems theory and electrical network theory, where a cascade decomposition of an input-output system or a network is related to a factorization of the associated transfer function. Canonical factorization has a long and interesting history which starts in the theory of convolution equations. Solving Wiener-Hopf integral equations is closely related to canonical factorization. The problem of canonical factorization also appears in other branches of applied analysis and in mathematical systems theory, in H -control theory in particular.
Factorization of operators -- Congresses. --- Factorization of operators. --- Operator theory. --- State-space methods. --- Factorization of operators --- State-space methods --- Operator theory --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Spectral theory (Mathematics) --- Operators, Factorization of --- Mathematics. --- Matrix theory. --- Algebra. --- Functions of complex variables. --- Operations research. --- Management science. --- Operator Theory. --- Linear and Multilinear Algebras, Matrix Theory. --- Operations Research, Management Science. --- Functions of a Complex Variable. --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Factorization (Mathematics) --- Factors (Algebra) --- Wiener-Hopf operators --- Complex variables --- Elliptic functions --- Functions of real variables --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Mathematical analysis
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