Factorization of Matrix and Operator Functions: The State Space Method

Harm Bart

ISBN 10: 3764382678 / ISBN 13: 9783764382674

Editore: Birkhäuser Basel, 2007

Riguardo questo articolo

Druck auf Anfrage Neuware - Printed after ordering - Thepresentbookdealswithvarioustypesoffactorizationproblemsformatrixand operator functions. The problems appear in di erent areasof mathematics and its applications. A uni ed approach to treat them is developed. The main theorems yield explicit necessaryand su cient conditions for the factorizations to exist and explicit formulas for the corresponding factors. Stability of the factors relative to a small perturbation of the original function is also studied in this book. The unifying theory developed in the book is based on a geometric approach which has its origins in di erent elds. A number of initial steps can be found in: (1) the theory of non-selfadjoint operators, where the study of invariant s- spaces of an operator is related to factorization of the characteristic matrix or operator function of the operator involved, (2) mathematical systems theory and electrical network theory, where a cascade decomposition of an input-output system or a network is related to a fact- ization of the associated transfer function, and (3) thefactorizationtheoryofmatrixpolynomialsintermsofinvariantsubspaces of a corresponding linearization. In all three cases a state space representation of the function to be factored is used, and the factors are expressed in state space form too. We call this approach the state space method. It hasa largenumber of applications.For instance, besides the areasreferred to above, Wiener-Hopf factorizations of some classes of symbols can also be treated by the state space method.

Codice articolo 9783764382674

Dati bibliografici

• Titolo: Factorization of Matrix and Operator Functions: The State Space Method
• Editore: Birkhäuser Basel
• Data di pubblicazione: 2007
• Lingua: Inglese
• ISBN 10: 3764382678
• ISBN 13: 9783764382674
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 250 L x 175 A x 29 P (millimetri) 250 millimetri di larghezza per 175 millimetri di altezza per 29 millimetri di profondità
• Peso: 916 grammi

Descrizione articolo

Riassunto

This book delineates the various types of 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, and the theory of job scheduling in operations research. The book presents 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.

Dalla quarta di copertina

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.