### Abstract

Suppose G is a singular matrix function on a simple, closed, rectifiable contour F. We present a necessary and sufficient condition for normal solvability of the Riemann problem with coefficient G in the case where G admits a spectral (or generalized Wiener-Hopf) factorization G_{+}ΛG_{-} with G^{±1} essentially bounded. The boundedness of G^{±1} is not required when Γ takes injective values a.e. on F.

Original language | English (US) |
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Pages (from-to) | 815-826 |

Number of pages | 12 |

Journal | Proceedings of the American Mathematical Society |

Volume | 125 |

Issue number | 3 |

State | Published - Dec 1 1997 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*125*(3), 815-826.

**On normal solvability of the riemann problem with singular coefficient.** / Rakowski, M.; Spitkovsky, Ilya.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 125, no. 3, pp. 815-826.

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TY - JOUR

T1 - On normal solvability of the riemann problem with singular coefficient

AU - Rakowski, M.

AU - Spitkovsky, Ilya

PY - 1997/12/1

Y1 - 1997/12/1

N2 - Suppose G is a singular matrix function on a simple, closed, rectifiable contour F. We present a necessary and sufficient condition for normal solvability of the Riemann problem with coefficient G in the case where G admits a spectral (or generalized Wiener-Hopf) factorization G+ΛG- with G±1 essentially bounded. The boundedness of G±1 is not required when Γ takes injective values a.e. on F.

AB - Suppose G is a singular matrix function on a simple, closed, rectifiable contour F. We present a necessary and sufficient condition for normal solvability of the Riemann problem with coefficient G in the case where G admits a spectral (or generalized Wiener-Hopf) factorization G+ΛG- with G±1 essentially bounded. The boundedness of G±1 is not required when Γ takes injective values a.e. on F.

UR - http://www.scopus.com/inward/record.url?scp=33646966783&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646966783&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33646966783

VL - 125

SP - 815

EP - 826

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 3

ER -