商品簡介
This book deals with canonical factorization of matrix and operator functions that appear in state space form or that can be transformed into such a form. A unified geometric approach is used. The main results are all expressed explicitly in terms of matrices or operators, which are parameters of the state space representation. The applications concern different classes of convolution equations: the transport equation, singular integral equations, Wiener-Hopf equations with symbols analytic in a strip, and equations involving factorization of non-proper rational matrix functions. The analysis of canonical factorization for functions with symmetries, including spectral and J-spectral factorizations, related Ricatti equations, and elements of H-infinity control theory are also main topics.
This is the second book written by the four authors in which the state space factorization method is systematically used and developed further. In their first book, Factorization of Matrix and Operator Functions: The State Space Method, released in 2007 as volume 178 of this series, the emphasis is on non-canonical factorizations and degree one factorizations, in particular. The present volume concentrates on canonical factorization and its applications. Both volumes together present a rich and far reaching update of the monograph written by the first three authors in 1979 and published as the first book in this series.
The text is largely self-contained and will be of interest to experts and students in mathematics, sciences, and engineering.
