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

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1989-0961416-3
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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  • [N] R. Nevanlinna, Analytic functions, Springer-Verlag, New York, (1970), pp. 108-111. MR 0279280 (43:5003)
  • [P] I. I. Privalov, Randeigenschaften analytischer Funktionen, VEB Deutscher Verlag der Wissenschaften, Berlin, 1956, pp. 129-130. MR 0083565 (18:727f)

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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

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