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A fluxintegral theorem for functions which have harmonic support


Author: Guy Johnson
Journal: Trans. Amer. Math. Soc. 98 (1961), 163-185
MSC: Primary 31.15
DOI: https://doi.org/10.1090/S0002-9947-1961-0125241-2
MathSciNet review: 0125241
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  • [1] M. G. Arsove, Functions representable as differences of subharmonic functions, Trans. Amer. Math. Soc. vol. 75 (1953) pp. 327-365. MR 0059416 (15:526d)
  • [2] E. F. Beckenbach, Generalized convex functions, Bull. Amer. Math. Soc. vol. 43 (1937) pp. 363-371. MR 1563543
  • [3] F. F. Bonsall, The characterization of generalized convex functions, Quart. J. Math. Oxford Ser. (2) vol. 1 (1950) pp. 100-111. MR 0036273 (12:83a)
  • [4] H. E. Bray, A Green's theorem in terms of Lebesgue integrals, Ann. of Math. vol. 21 (1920) pp. 141-156. MR 1503612
  • [5] C. Carathéodory, Theory of functions of a complex variable, vol. 1, New York, Chelsea, 1954.
  • [6] P. J. Daniell, A general form of Green's theorem, Bull. Amer. Math. Soc. vol. 25 (1919) pp. 353-357. MR 1560201
  • [7] G. C. Evans, Fundamental points of potential theory, The Rice Institute Pamphlet, no. 4, vol. 7, 1920, pp. 252-329.
  • [8] -, The logarithmic potential, New York, Amer. Math. Soc. Colloquium Publications, vol. 6, 1927.
  • [9] G. M. Golusin, Geometrische Funktionentheorie, Berlin, Deutscher Verlag der Wissenschaften, 1957. MR 0089896 (19:735e)
  • [10] G. Johnson, Functions which have harmonic support, Trans. Amer. Math. Soc. vol. 92 (1959) pp. 302-321. MR 0108652 (21:7367)
  • [11] D. Menchoff, Les conditions de monogénéité, Actualités Sci. Ind. no. 329 (1936) pp. 1-50.
  • [12] M. M. Peixoto, Generalized convex functions und second order differential inequalities, Bull. Amer. Math. Soc. vol. 55 (1949) pp. 563-572. MR 0029949 (10:686a)
  • [13] G. Pólya, Untersuchen über Lücken und Singularitäten von Potenzreihen, Math. Z. vol. 29 (1929) pp. 549-640.
  • [14] C. de la Vallée Poussin, Sur l'intégrale de Lebesgue, Trans. Amer. Math. Soc. vol. 16 (1915) pp. 435-501. MR 1501024
  • [15] -, Le potentiel logarithmic, Paris, Gauthier-Villars, 1949.
  • [16] H. Rademacher, Über partielle und totale differenzierbarkeit von Funktionen mehrer Variablen, Math. Ann. vol. 79 (1919) p. 340. MR 1511935
  • [17] T. Radó, Subharmonic functions, Berlin, Springer, 1937.
  • [18] F. Riesz, Sur les fonctions subharmoniques et leur rapport à la théorie du potentiel, seconde partie, Acta Math. vol. 54 (1930) pp. 321-360. MR 1555311
  • [19] G. Valiron, Remarques sur certaines fonctions convexes, Proc. Phys. Math. Soc. Japan ser. 3 vol. 13 (1931) pp. 19-38.

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DOI: https://doi.org/10.1090/S0002-9947-1961-0125241-2
Article copyright: © Copyright 1961 American Mathematical Society

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