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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Uniqueness of bounded harmonic functions
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by Marvin Ortel and Walter Schneider PDF
Proc. Amer. Math. Soc. 107 (1989), 937-942 Request permission

Abstract:

We prove the following theorem: A bounded harmonic function is identically zero if it tends to zero at a certain rate along a set of radii of positive measure. In particular, this uniqueness theorem does not require that the function in question have smooth boundary values or restricted derivatives.
References
    A. Beurling, Etudes sur un problème de majoration, Thèse, Uppsala, 1930.
  • Rolf Nevanlinna, Analytic functions, Die Grundlehren der mathematischen Wissenschaften, Band 162, Springer-Verlag, New York-Berlin, 1970. Translated from the second German edition by Phillip Emig. MR 0279280
  • I. I. Priwalow, Randeigenschaften analytischer Funktionen, Hochschulbücher für Mathematik, Band 25, VEB Deutscher Verlag der Wissenschaften, Berlin, 1956 (German). Zweite, unter Redaktion von A. I. Markuschewitsch überarbeitete und ergänzte Auflage. MR 0083565
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 107 (1989), 937-942
  • MSC: Primary 31A20; Secondary 31A15, 31A25
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0961416-3
  • MathSciNet review: 961416