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