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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Pluriharmonic functions in balls
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by Walter Rudin
Proc. Amer. Math. Soc. 62 (1977), 44-46
DOI: https://doi.org/10.1090/S0002-9939-1977-0422687-7
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Abstract:

It is proved that a function is pluriharmonic in the open unit ball of ${{\mathbf {C}}^n}$ if and only if it is harmonic with respect to both the ordinary Laplacian and the invariant Laplace-Beltrami operator.
References
  • Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. MR 0180696
  • E. M. Stein, Boundary behavior of holomorphic functions of several complex variables, Mathematical Notes, No. 11, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. MR 0473215
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Bibliographic Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 62 (1977), 44-46
  • MSC: Primary 32F05; Secondary 31C10
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0422687-7
  • MathSciNet review: 0422687