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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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A simple proof for Schur’s theorem
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by R. A. Kortram PDF
Proc. Amer. Math. Soc. 129 (2001), 3211-3212 Request permission

Abstract:

In 1917 Schur gave a characterization of bounded analytic functions on the unit disc. We present a simple proof.
References
  • J. Campschroer, Inverse coefficients and symmetrization of univalent functions. Doctoral dissertation. University of Nijmegen 1984.
  • John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
  • I. Schur, Über Potenzreihen die im Innern des Einheitskreises beschränkt sind. J. Reine Angew. Math. 147 (1917), 205-232.
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Additional Information
  • R. A. Kortram
  • Affiliation: Department of Mathematics, University of Nijmegen, 6525 ED Nijmegen, The Netherlands
  • Email: kortram@sci.kun.nl
  • Received by editor(s): February 15, 2000
  • Published electronically: May 21, 2001
  • Communicated by: Juha M. Heinonen
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 3211-3212
  • MSC (2000): Primary 30B10
  • DOI: https://doi.org/10.1090/S0002-9939-01-06199-8
  • MathSciNet review: 1844995