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.
General
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