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引用次数: 0
摘要
摘要域$\Omega\subet{\mathbb C}^D$的子集${\mathcal D}$为分析函数$f:\Omega\to\overline{\math bb D}}$确定,如果分析函数$g:\Omega\rightarrow\overline{\mathbbD}}$与${\math cal D}$上的f重合,则整个$\Omega上的f等于f。这个注释找到了对称化bidisk的子集被确定的几个充分条件。对于任何$N\geq1$,构造了一个由$N^2-N+1$多个点组成的集合,该集合确定了具有度约束的任何有理内函数。我们还研究了对称二次空间与一些特殊代数变种的交集何时可以确定有理内函数。
Determining sets for holomorphic functions on the symmetrized bidisk
Abstract A subset
${\mathcal D}$
of a domain
$\Omega \subset {\mathbb C}^d$
is determining for an analytic function
$f:\Omega \to \overline {{\mathbb D}}$
if whenever an analytic function
$g:\Omega \rightarrow \overline {{\mathbb D}}$
coincides with f on
${\mathcal D}$
, equals to f on whole
$\Omega $
. This note finds several sufficient conditions for a subset of the symmetrized bidisk to be determining. For any
$N\geq 1$
, a set consisting of
$N^2-N+1$
many points is constructed which is determining for any rational inner function with a degree constraint. We also investigate when the intersection of the symmetrized bidisk intersected with some special algebraic varieties can be determining for rational inner functions.
期刊介绍:
The Canadian Mathematical Bulletin was established in 1958 to publish original, high-quality research papers in all branches of mathematics and to accommodate the growing demand for shorter research papers. The Bulletin is a companion publication to the Canadian Journal of Mathematics that publishes longer papers. New research papers are published continuously online and collated into print issues four times each year.
To be submitted to the Bulletin, papers should be at most 18 pages long and may be written in English or in French. Longer papers should be submitted to the Canadian Journal of Mathematics.
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Les textes présentés au BCM doivent compter au plus 18 pages et être rédigés en anglais ou en français. C’est le Journal canadien de mathématiques qui reçoit les articles plus longs.