On the Harmonic Measure of Self-Similar Sets on the Plane
On the Harmonic Measure of Self-Similar Sets on the Plane
复制标题
平面上自相似集的调和测度
DOI：
--
复制
发表时间：
1992
期刊：
影响因子：
--
通讯作者：
A. Volberg
中科院分区：
文献类型：
--
作者：
A. Volberg
调和测度是一维复分析的基本对象之一。近年来，由于Makarov [1]，Carleson [2]和Jones，Wolff [3]的工作，使得较一般的平面集的调和测度的结构变得更加容易理解。在这个问题上，（几乎）独立随机变量和域的绿色函数的行为之间的深刻类比起着至关重要的作用。我们建议读者参考[15]以了解更多细节。如果研究调和测度的域具有规则的自相似结构，这种类比就变得更加明显。遍历理论的方法在这种情况下是相关的，参见例如[2]，[4]，[5]，[6]。
Harmonic measure is one of the basic objects of one dimensional complex analysis. Recently the structure of harmonic measure of rather general plane sets became much more comprehensible due to works of Makarov [1], Carleson [2] and Jones, Wolff [3]. The deep analogy between the behaviour of sums of (almost) independent random variables and the behaviour of the Green function of a domain plays a crucial role in this subject. We refer the reader to [15] for more details. This analogy becomes still more conspicuous if the domain for which the harmonic measure is investigated has regular self-similar structure. The methods of ergodic theory turn out to be relevant in this case, see e.g. [2], [4], [5], [6].