An Observation about Frostman Shifts
An Observation about Frostman Shifts
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关于弗罗斯特曼转变的观察
DOI：
10.1007/bf03321635
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发表时间：
2007
影响因子：
2.1
通讯作者：
W. Ross
中科院分区：
文献类型：
--
作者：
A. Matheson;W. Ross
Frostman的一个经典定理说，如果B是Blaschke积（或任何内部函数），则它的Frostman移位$$B_w = \left（{B - w} \right）\left（{1 - \bar wB} \right）^{ - 1}$$是Blaschke积，对所有|W| < 1，除了可能对于对数容量为零的集合中的w。如果B是Frostman Blaschke积，等价于单位圆上测度的Cauchy变换空间的内乘子，我们证明了对所有|W| < 1，Bw确实是另一个Frostman Blaschke产品。
A classical theorem of Frostman says that if B is a Blaschke product (or any inner function), then its Frostman shifts $$B_w = \left( {B - w} \right)\left( {1 - \bar wB} \right)^{ - 1}$$ are Blaschke products for all |w| < 1 except possibly for w in a set of logarithmic capacity zero. If B is a Frostman Blaschke product, equivalently an inner multiplier for the space of Cauchy transforms of measures on the unit circle, we show that for all |w| < 1, Bw is indeed another Frostman Blaschke product.