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Spectral factorization of measurable rectangular matrix functions and the vector-valued Riemann problem. (English) Zbl 0869.30028

The authors consider the problem of factorization of measurable singular matrix valued functions under sufficiently general assumptions according the contours. In particular, they assume that the contour may be a simple closed rectifiable curve and show that such factorization has analogous properties as in the nonsingular case. The connection between this factorization and boundary vector-valued Riemann problem are also considered.

MSC:

30E25 Boundary value problems in the complex plane
47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)

Keywords:

Riemann problem
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