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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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 $\Gamma$.
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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