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

Marek Rakowski, Ilya Spitkovsky

Research output: Contribution to journalArticle

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
StatePublished - Jan 1 1996

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Spectral Factorization
Matrix Function
Cauchy Problem
Defects
Wiener-Hopf Factorization
Singular Functions
Singular matrix
Coefficient
Singular Values
Factorization
Uniqueness
Necessary Conditions
Closed
Sufficient Conditions

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Spectral factorization of measurable rectangular matrix functions and the vector-valued Riemann problem. / Rakowski, Marek; Spitkovsky, Ilya.

In: Revista Matematica Iberoamericana, Vol. 12, No. 3, 01.01.1996, p. 669-696.

Research output: Contribution to journalArticle

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