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
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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