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Plurisubharmonic functions associated with uniform algebras


Author: Donna Kumagai
Journal: Proc. Amer. Math. Soc. 87 (1983), 303-308
MSC: Primary 46J10; Secondary 32F05
DOI: https://doi.org/10.1090/S0002-9939-1983-0681839-4
MathSciNet review: 681839
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Abstract: We have proved earlier that a certain class of functions, which is useful in the study of analytic structure associated with a uniform algebra, is plurisubharmonic, if the algebra satisfies Basener's conjecture. In this paper we prove the plurisubharmonicity of these functions without the hypothesis of Basener's conjecture.


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

  • [1] B. Aupetit and J. Wermer, Capacity and uniform algebras, J. Funct. Anal. 28 (1978), 386-400. MR 496966 (80a:31001)
  • [2] B. Aupetit, Analytic multivalued functions in Banach algebras and uniform algebras, Adv. in Math. 44 (1982), 18-60. MR 654547 (84b:46059)
  • [3] D. Kumagai, The measure spectrum of a uniform algebra and subharmonicity, Canad. J. Math. (to appear). MR 663309 (84a:46109)
  • [4] -, Subharmonic functions and uniform algebras, Proc. Amer. Math. Soc. 78 (1980), 23-29. MR 548077 (80k:46055)
  • [5] R. F. Basener, A generalized Shilov boundary and analytic structure, Proc. Amer. Math. Soc. 47 (1975), 98-104. MR 0352990 (50:5476)
  • [6] Z. Slodkowski, On subharmonicity of capacity of spectrum, Proc. Amer. Math. Soc. 81 (1981), 243-249. MR 593466 (83d:46062)
  • [7] V. N. Seničkin, Subharmonic functions and analytic structure in the maximal ideal space of a uniform algebra, Math. USSR-Sb. 36 (1980).
  • [8] J. Wermer, Subharmonicity and hulls, Pacific J. Math. 8 (1975), 283-290. MR 0393567 (52:14376)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0681839-4
Keywords: Plurisubharmonicity, subharmonicity, uniform algebras, analytic structure, Shilov boundary
Article copyright: © Copyright 1983 American Mathematical Society

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