### Abstract

We define spectral factorization in L_{p} (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 L_{p}.

Original language | English (US) |
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Pages (from-to) | 669-696 |

Number of pages | 28 |

Journal | Revista Matematica Iberoamericana |

Volume | 12 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 1 1996 |

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### ASJC Scopus subject areas

- Mathematics(all)