Spectral factorization of measurable rectangular matrix functions and the vector-valued Riemann problem

Marek Rakowski, Ilya Spitkovsky

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Abstract

We define spectral factorization in Lp (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 coefficient. Based on the Riemann problem, we obtain a necessary and sufficient condition for existence of a spectral factorization in Lp.

Original languageEnglish (US)
Pages (from-to)669-696
Number of pages28
JournalRevista Matematica Iberoamericana
Volume12
Issue number3
DOIs
Publication statusPublished - Jan 1 1996

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ASJC Scopus subject areas

  • Mathematics(all)

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