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Proceedings of the American Mathematical Society

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



Short proofs of three theorems on harmonic functions

Authors: H. P. Boas and R. P. Boas
Journal: Proc. Amer. Math. Soc. 102 (1988), 906-908
MSC: Primary 31B05; Secondary 30D30
MathSciNet review: 934865
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Abstract: We present elementary proofs--shorter than any others that we know--for three related theorems.

References [Enhancements On Off] (What's this?)

  • [1] N. G. Chebotarev and N. N. Meĭman, The Routh-Hurwitz problem for polynomials and entire functions, Trudy Mat. Inst. Steklov. 26 (1949). (Russian)
  • [2] A. Dinghas, Über positive harmonische Funktionen in einem Halbraum, Math. Z. 46 (1940), 559-570. MR 0003334 (2:202d)
  • [3] Ü. Kuran, Harmonic majorizations in half-balls and half-spaces, Proc. London Math. Soc. 21 (1970), 614-636. MR 0315148 (47:3697)
  • [4] L. H. Loomis and D. V. Widder, The Poisson integral representation of functions which are positive and harmonic in a half-plane, Duke Math. J. 9 (1942), 643-645. MR 0007200 (4:101e)
  • [5] M. Tideman, Elementary proof of a uniqueness theorem for positive harmonic functions, Nordisk. Mat. Tidskrift 2 (1954), 95-96. MR 0063497 (16:129g)
  • [6] N. Tschebotareff, Über Realität von Nullstellen ganzer transzendenter Funktionen, Math. Ann. 99 (1928), 660-686. MR 1512472
  • [7] M. Tsuji, On a positive harmonic function in a half-plane, Japan. J. Math. 15 (1939), 277-285. MR 0068047 (16:819g)

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Keywords: Positive harmonic functions, Liouville's theorem, meromorphic functions
Article copyright: © Copyright 1988 American Mathematical Society

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