有理内函数的Clark测度

IF 0.8 3区数学 Q2 MATHEMATICS

Michigan Mathematical Journal Pub Date : 2021-01-02 DOI:10.1307/mmj/20216046

K. Bickel, J. Cima, A. Sola

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引用次数: 7

摘要

本文分析了双盘上与双变量有理内函数相关的克拉克测度和克拉克等距的精细结构。在度(n, 1)的情况下，我们给出了一般和例外Clark测度的支持度和权值的完整描述，刻画了相关嵌入算子是酉的情况，并给出了这些嵌入算子的公式。我们还强调了我们的结果与Agler分解的结构和2-环面上正多谐测度集的极值点的研究之间的联系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Clark Measures for Rational Inner Functions

We analyze the fine structure of Clark measures and Clark isometries associated with two-variable rational inner functions on the bidisk. In the degree (n, 1) case, we give a complete description of supports and weights for both generic and exceptional Clark measures, characterize when the associated embedding operators are unitary, and give a formula for those embedding operators. We also highlight connections between our results and both the structure of Agler decompositions and study of extreme points for the set of positive pluriharmonic measures on 2-torus.

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来源期刊

Michigan Mathematical Journal 数学-数学

CiteScore

1.20

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Michigan Mathematical Journal is available electronically through the Project Euclid web site. The electronic version is available free to all paid subscribers. The Journal must receive from institutional subscribers a list of Internet Protocol Addresses in order for members of their institutions to have access to the online version of the Journal.