Wiener-Hopf Factorization of a Class of Matrix Functions and Corona Theorem

摘要

By using the Riemann-Hilbert method and the Corona theorem, Wiener-Hopf factorization for a class of matrix functions is studied. Under appropriate assumption, a sufficient and neces-sary condition for the existence of the matrix function admitting canonical factorization is obtained and the solution to a class of non-linear Riemann-Hilbert problems is also given. Furthermore, by means of non-standard Corona theorem partial estimation of the general factorization can be obtained.