Introduction

Abstract

This monograph presents a unified approach for solving canonical factorization problems for different classes of matrix and operator functions. The notion of canonical factorization originates from the theory of convolution equations. For instance, canonical factorization, provided it exists, allows one to invert Wiener-Hopf, Toeplitz and singular integral operators, and when the factors are known one can also build explicitly the inverses of these operators. The problem of canonical factorization also appears in various branches of applied analysis, in linear transport theory, in interpolation theory, in mathematical systems theory, in particular, in H_∞-control theory.