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Proceedings of the American Mathematical Society

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Uniqueness of bounded harmonic functions


Authors: Marvin Ortel and Walter Schneider
Journal: Proc. Amer. Math. Soc. 107 (1989), 937-942
MSC: Primary 31A20; Secondary 31A15, 31A25
MathSciNet review: 961416
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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 [Enhancements On Off] (What's this?)

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  • [P] I. I. Priwalow, Randeigenschaften analytischer Funktionen, Zweite, unter Redaktion von A. I. Markuschewitsch überarbeitete und ergänzte Auflage. Hochschulbücher für Mathematik, Bd. 25, VEB Deutscher Verlag der Wissenschaften, Berlin, 1956 (German). MR 0083565

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0961416-3
Keywords: Bounded harmonic functions, radial limits, boundary value problems
Article copyright: © Copyright 1989 American Mathematical Society