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We define spectral factorization in L (or a generalized Wiener-Hopf factorization) of a measurable singular matrix function on a simple closed rectifiable contour Γ. Such factorization has the same uniqueness properties as in the nonsingular case. We discuss basic properties of the vector valued Riemann problem whose coefficient takes singular values almost everywhere on Γ. In particular, we introduce defect numbers for this problem which agree with the usual defect numbers in the case of a nonsingular...
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