## On normal solvability of the Riemann problem with singular coefficient

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- by M. Rakowski and I. Spitkovsky PDF
- Proc. Amer. Math. Soc.
**125**(1997), 815-826 Request permission

## Abstract:

Suppose $G$ is a singular matrix function on a simple, closed, rectifiable contour $\Gamma$. 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 $G_{+} \Lambda G_{-}$ with $G_{-}^{\pm 1}$ essentially bounded. The boundedness of $G_{-}^{\pm 1}$ is not required when $G$ takes injective values a.e. on $\Gamma$.## References

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## Additional Information

**M. Rakowski**- Affiliation: Department of Mathematics, The Ohio State University, Columbus, Ohio 43210
- Email: rakowski@math.ohio-state.edu
**I. Spitkovsky**- Affiliation: Department of Mathematics, The College of William and Mary, Williamsburg, Virginia 23187-8795
- MR Author ID: 191035
- ORCID: 0000-0002-1411-3036
- Email: ilya@cs.wm.edu
- Received by editor(s): September 8, 1995
- Additional Notes: This research was partially supported by the NSF Grants DMS-9302706 and DMS-9401848.
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**125**(1997), 815-826 - MSC (1991): Primary 45E05, 45F15, 47A68
- DOI: https://doi.org/10.1090/S0002-9939-97-03631-9
- MathSciNet review: 1353395