一般双次数与更高维情形下有理内函数的 Clark 测度 II
Clark measures for rational inner functions II: general bidegrees and higher dimensions
AI总结：
本文研究双圆盘二元及高维无奇性有理内函数的 Clark 测度，刻画其支撑、权重、酉嵌入条件，并揭示权重消失与奇性接触阶的关系。
摘要：
我们研究与双圆盘上一般的二元有理内函数（RIF）相关联的 Clark 测度，其中包括具有奇性的函数，并研究与一般的无奇性 d 元有理内函数相关联的 Clark 测度。我们利用相应 RIF 的水平集和偏导数，对此类 Clark 测度的支撑集和权重给出精确描述。在二元情形中，我们刻画相应的 Clark 嵌入何时为酉算子；对于一般参数值，我们将二元权重的消失与相应 RIF 在奇性处的接触阶联系起来。
英文摘要：
We study Clark measures associated with general two-variable rational inner functions (RIFs) on the bidisk, including those with singularities, and with general $d$-variable rational inner functions with no singularities. We give precise descriptions of support sets and weights for such Clark measures in terms of level sets and partial derivatives of the associated RIF. In two variables, we characterize when the associated Clark embeddings are unitary, and for generic parameter values, we relate vanishing of two-variable weights with the contact order of the associated RIF at a singularity.
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