Wiener-Hopf factorization of piecewise meromorphic matrix-valued functions

Abstract

Let D+ be amultiply connected domain bounded by a contour Γ, let D- be the complement of D+ ∪ Γ in ℂ̄ = ℂ ∪, and a(t) be acontinuous invertible matrix-valued function on which can be meromorphically extended into the open disconnected set (as apiecewise meromorphic matrix-valued function). An explicit solution of the Wiener-Hopf factorization problem for is obtained and the partial factorization indices of are calculated. Here an explicit solution of afactorization problem is meant in the sense of reducing it to the investigation of finitely many systems of linear algebraic equations with matrices expressed in closed form, that is, in quadratures. Bibliography: 15 titles. © 2009 Russian Academy of Sciences, (DoM) and London Mathematical Society.