[Annotatie]: The present book deals with factorization problems for matrix and operator functions. The problems originate from, or are motivated by, the theory of non-selfadjoint operators, the theory of matrix polynomials, mathematical systems and control theory, the theory of Riccati equations, inversion of convolution operators, theory of job scheduling in operations research. The book systematically employs a geometric principle of factorization which has its origins in the state space theory of linear input-output systems and in the theory of characteristic operator functions. This principle allows one to deal with different factorizations from one point of view. Covered are canonical factorization, minimal and non-minimal factorizations, pseudo-canonical factorization, and various types of degree one factorization. Considerable attention is given to the matter of stability of factorization which in terms of the state space method involves stability of invariant subspaces.invariant subspaces. TOC:Preface.- Motivating Problems.- Operator Nodes, Systems, Operations on Systems.- Realization and Linearization.- Factorization and Riccati Equations.- Canonical Factorization.- Minimal Systems.- Minimal Realization and Pole-Zero Structure.- Degree One Factors.- Factorization and Job Scheduling.- Stability of Factorization and of Invariant Subspaces.- Factorization of Real Matrix Functions.- Bibliography.- Index. [Inhoudsopgave]: PrefacexiIntroduction1(6)Part I Motivating Problems, Systems and RealizationsMotivating ProblemsLinear time invariant systems and cascade connection7(4)Characteristic operator functions and invariant subspaces (1)11(3)Characteristic operator functions and invariant subspaces (2)14(3)Factorization of monic matrix polynomials17(1)Wiener-Hopf integral operators and factorization18(3)Block Toeplitz equations and factorization21(4)Notes23(2)Operator Nodes, Systems, and Operations on SystemsOperator nodes, systems and transfer functions25(2)Inversion27(3)Products30(2)Factorization and matching of invariant subspaces32(5)Factorization and inversion revisited37(12)Notes48(1)Various Classes of SystemsBrodskii systems49(1)Krein systems50(1)Unitary systems51(2)Monic systems53(4)Polynomial systems57(1)Mobius transformation of systems58(7)Notes64(1)Realization and Linearization of Operator FunctionsRealization of rational operator functions65(2)Realization of analytic operator functions67(2)Linearization69(4)Linearization and Schur complements73(4)Notes76(1)Factorization and Riccati EquationsAngular subspaces and angular operators77(2)Angular subspaces and the algebraic Riccati equation79(1)<TD WIDTH=60
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