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On normal solvability of the Riemann problem with singular coefficient


Authors: M. Rakowski and I. Spitkovsky
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
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Abstract | References | Similar Articles | Additional Information

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 $\Gamma$.


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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
Article copyright: © Copyright 1997 American Mathematical Society