Factorization of Matix and Operator Functions: The State Space Method - Couverture rigide

Livre 24 sur 132: Operator Theory: Advances and Applications

Bart, Harm; Gohberg, Israel; Kaashoek, Marinus A.; Ran, André C.M.

 
9783764382674: Factorization of Matix and Operator Functions: The State Space Method
Couverture rigide
ISBN 10 : 3764382678 ISBN 13 : 9783764382674
Editeur : Birkhauser Verlag AG, 2007

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Éditeur
Birkhauser Verlag AG
Date d'édition
2007
Langue
anglais
ISBN 10 
3764382678
ISBN 13 
9783764382674
Reliure
Relié
Nombre de pages
412
Coordonnées du fabricant
non disponible
Personne responsable
non disponible

Autres éditions populaires du même titre

9783764391911: Factorization of Matrix and Operator Functions: The State Space Method

Edition présentée

ISBN 10 :  376439191X ISBN 13 :  9783764391911
Editeur : Springer, 2008
Couverture souple