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

Marek Rakowski; Ilya Spitkovsky

Revista Matemática Iberoamericana (1996)

- Volume: 12, Issue: 3, page 669-696
- ISSN: 0213-2230

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topRakowski, Marek, and Spitkovsky, Ilya. "Spectral factorization of measurable rectangular matrix functions and the vector-valued Riemann problem.." Revista Matemática Iberoamericana 12.3 (1996): 669-696. <http://eudml.org/doc/39522>.

@article{Rakowski1996,

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.},

author = {Rakowski, Marek, Spitkovsky, Ilya},

journal = {Revista Matemática Iberoamericana},

keywords = {Matrices; Factorización; Problema de Riemann; Continuidad; Riemann problem},

language = {eng},

number = {3},

pages = {669-696},

title = {Spectral factorization of measurable rectangular matrix functions and the vector-valued Riemann problem.},

url = {http://eudml.org/doc/39522},

volume = {12},

year = {1996},

}

TY - JOUR

AU - Rakowski, Marek

AU - Spitkovsky, Ilya

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

JO - Revista Matemática Iberoamericana

PY - 1996

VL - 12

IS - 3

SP - 669

EP - 696

AB - 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.

LA - eng

KW - Matrices; Factorización; Problema de Riemann; Continuidad; Riemann problem

UR - http://eudml.org/doc/39522

ER -

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