Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Normal families of subharmonic functions


Author: Maynard G. Arsove
Journal: Proc. Amer. Math. Soc. 7 (1956), 115-126
MSC: Primary 31.0X
DOI: https://doi.org/10.1090/S0002-9939-1956-0078463-7
MathSciNet review: 0078463
Full-text PDF

References | Similar Articles | Additional Information

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

  • [1] N. Aronszajn, La théorie des noyaux reproduisants et ses applications: première partie, Proc. Cambridge Philos. Soc. vol. 39 (1943) pp. 133-153. MR 0008639 (5:38e)
  • [2] -, Green's functions and reproducing kernels, Proceedings of the Symposium on Spectral Theory and Differential Problems, 1951, pp. 355-411.
  • [3] M. G. Arsove, Functions representable as differences of subharmonic functions, Trans. Amer. Math. Soc. vol. 75 (1953) pp. 327-365. MR 0059416 (15:526d)
  • [4] -, Functions of potential type, Trans. Amer. Math. Soc. vol. 75 (1953) pp. 526-551. MR 0060075 (15:622c)
  • [5] -, The Looman-Menchoff theorem and some subharmonic function analogues, Proc. Amer. Math. Soc. vol. 6 (1955) pp. 94-105. MR 0069965 (16:1108b)
  • [6] S. Bergman, The kernel function and conformal mapping, Mathematical Surveys, vol. 5, American Mathematical Society, 1950. MR 0038439 (12:402a)
  • [7] -, Functions of the extended class in the theory of functions of several complex variables, Trans. Amer. Math. Soc. vol. 63 (1948) pp. 423-447. MR 0025583 (10:30b)
  • [8] S. Bergman and M. Schiffer, Kernel functions in the theory of partial differential equations of elliptic type, Duke Math. J. vol. 15 (1948) pp. 535-566. MR 0025662 (10:42b)
  • [9] O. Frostman, Distributions de masses normées par la métrique de $ {L^p}$, Lund Univ. Math. Sem. supplementary vol. dedicated to Marcel Riesz (1952) pp. 90-100. MR 0054794 (14:980d)
  • [10] O. D. Kellog, Potential theory, Berlin, 1929.
  • [11] P. Montel, Sur quelques familles de fonctions harmoniques, Fund. Math. vol. 25 (1935) pp. 388-407.
  • [12] -, Sur les fonctions convexes et les fonctions sousharmoniques, J. de Math. vol. 7 (1928) pp. 29-60.
  • [13] A. D. Myškis, A theorem on the convergence of a sequence of functions, Uspehi Matematičeskih Nauk vol. 7 (1952) pp. 186-190 (Russian). MR 0047854 (13:942h)
  • [14] T. Radó, Subharmonic functions, Berlin, 1937.
  • [15] M. O. Reade, On averages of Newtonian potentials, Bull. Amer. Math. Soc. vol. 53 (1947) pp. 321-331. MR 0020176 (8:514b)
  • [17] L. Schwartz, Théorie des distributions, vol. II, Actualités Scientifiques et Industrielles, no. 1122, 1951. MR 0042610 (13:138a)
  • [18] J. M. Thompson, Distributions of mass for averages of Newtonian potential functions, Bull. Amer. Math. Soc. vol. 41 (1935) pp. 744-752. MR 1563179

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 31.0X

Retrieve articles in all journals with MSC: 31.0X


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1956-0078463-7
Article copyright: © Copyright 1956 American Mathematical Society

American Mathematical Society