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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Radial limits of $n$-subharmonic functions in the polydisc
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by W. C. Nestlerode and M. Stoll
Trans. Amer. Math. Soc. 279 (1983), 691-703
DOI: https://doi.org/10.1090/S0002-9947-1983-0709577-4

Abstract:

We prove a relation between a certain weighted radial limit of an $n$-subharmonic function in the polydisc ${U^n}$ and the representing measure of its least $n$-harmonic majorant. We apply this result to functions in $N({U^n})$, the Nevalinna class of ${U^n}$. In particular, we obtain a necessary condition for a function to belong to the component of the origin in $N({U^n})$. These results are extensions of the work of J. H. Shapiro and A. L. Shields to $n > 1$.
References
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Bibliographic Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 279 (1983), 691-703
  • MSC: Primary 32A22; Secondary 42B25
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0709577-4
  • MathSciNet review: 709577