A Note on Projective Capacity
A Note on Projective Capacity
复制标题
关于投射能力的注释
DOI：
10.4153/cjm-1982-091-x
复制
发表时间：
1982
期刊：
影响因子：
--
通讯作者：
H. Alexander
中科院分区：
文献类型：
--
作者：
H. Alexander
介绍。在b[1]中，我们定义了cn中的容量。最近，Molzon， Shiffman和Sibony[8]引入了一种不同的容量，它对某些Bezout估计很有用。本文的目的是应用[1]的方法来研究[8]的容量。我们将沿着[1]的线，通过切比切夫多项式得到这个容量的等价定义。这个等效量的一半是由Sibony[9]独立获得的。为了建立这两种容量方法的完全等价性，需要在比一致代数更一般的情况下使用延森测度的概念。我们将考虑乘法半群的Jensen测度；这些是一组函数，其中只有乘法结构是假设的。将多项式壳的概念推广到关于多项式的乘法半群的壳也是有用的。然后我们可以将[1]的方法应用于这些半群。
Introduction. In [1] we defined a capacity in C n . Recently Molzon, Shiffman and Sibony [8] have introduced a different capacity which is useful for certain Bezout estimates. The object of this note is to apply the methods of [1] to study the capacity of [8]. We shall obtain an equivalent definition of this capacity via Tchebycheff polynomials, along the lines of [1]. Half of this equivalence was independently obtained by Sibony [9]. To establish the full equivalence of these two approaches to capacity a notion of Jensen measures in a setting more general than uniform algebras is needed. We shall consider Jensen measures for multiplicative semigroups; these are sets of functions in which only the multiplicative structure is postulated. It will also be useful to generalize the notion of polynomial hull in C n to a hull with respect to a multiplicative semigroup of polynomials. We can then adapt the approach of [1] to these semigroups.