全局$P$极值函数的乘积性质

Pub Date : 2021-11-30 DOI:10.7146/math.scand.a-129007

N. Q. Dieu, T. V. Long

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引用次数: 0

摘要

在这篇笔记中，我们建立了$P$极值函数的一个乘积性质，其精神与J. Siciak在Ann中给出的原乘积公式相同。Polon。数学。， 39(1981)， 175-211。因此，我们得到了这类极值函数的子层次集的凸性。此外，我们还推广了L. Bos和N. Levenberg在Comput中建立的$P$极值函数的乘积性质。功能的方法。理论18(2018)，361-388，后来由N. Levenberg和M. Perera在当代数学743(2020)，11-19中，其中不需要对$P$进行限制。

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Product property of global $P$-extremal functions

In this note, we establish a product property for $P$-extremal functions in the same spirit as the original product formula due to J. Siciak in Ann. Polon. Math., 39 (1981), 175–211. As a consequence, we obtain convexity for the sublevel sets of such extremal functions. Moreover, we also generalize the product property of $P$-extremal functions established by L. Bos and N. Levenberg in Comput. Methods Funct. Theory 18 (2018), 361–388, and later by N. Levenberg and M. Perera, in Contemporary Mathematics 743 (2020), 11–19, in which no restriction on $P$ is needed.

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