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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