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

Rakowski, 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 -