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Transactions of the American Mathematical Society

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Converses of Gauss' theorem on the arithmetic mean


Author: Oliver D. Kellogg
Journal: Trans. Amer. Math. Soc. 36 (1934), 227-242
MSC: Primary 31A05
DOI: https://doi.org/10.1090/S0002-9947-1934-1501739-0
MathSciNet review: 1501739
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  • [1] Evans, G. C., Application of Poincaré's sweeping-out process, Proceedings of the National Academy of Sciences, vol. 19 (1933), pp. 457-461.
  • [2] Kellogg, O. D., Foundations of Potential Theory, Berlin, 1929.
  • [3] -On the classical Dirichlet problem for general domains, Proceedings of the National Academy of Sciences, vol. 12 (1926), pp. 397-406.
  • [4] O. D. Kellogg, Recent progress with the Dirichlet problem, Bull. Amer. Math. Soc. 32 (1926), no. 6, 601–625. MR 1561275, https://doi.org/10.1090/S0002-9904-1926-04267-1
  • [5] -Unicité des fonctions harmoniques, Comptes Rendus de l'Académie des Sciences, vol. 187 (1928), pp. 526-527.
  • [6] Koebe, P., Herleitung der partiellen Differentialgleichung der Potentialfunktion aus der Integraleigenschaft, Sitzungsberichte der Berliner Mathematischen Gesellschaft, vol. 5 (1906), pp. 39-42.
  • [7] Lebesgue, H., Sur le problème de Dirichlet, Comptes Rendus de l'Académie des Sciences, vol. 154 (1912), pp. 335-337.
  • [8] Perkins, F. W., Sur la résolution du problème de Dirichlet par des médiations réitérées, ibid., vol. 184 (1927), pp. 182-183.
  • [9] Wiener, N., The Dirichlet problem, Journal of Mathematics and Physics, Massachusetts Institute of Technology, vol. 3 (1924), pp. 127-146.
  • [10] -Certain notions in potential theory, ibid., vol. 3 (1924), pp. 25-51.

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DOI: https://doi.org/10.1090/S0002-9947-1934-1501739-0
Article copyright: © Copyright 1934 American Mathematical Society