两个变量的实有理Herglotz-Nevanlinna函数及一类极值元
Real rational Herglotz-Nevanlinna functions in two variables and a class of extremals
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中文总结 AI 辅助
本文研究两个变量实有理Herglotz-Nevanlinna函数的极值性，给出显式表示测度公式，构造极值元族并发现Knese猜想反例，同时代数与几何地表征可约性。
中文摘要 AI 辅助
我们首先重新审视两个变量中Herglotz-Nevanlinna函数的表示测度所满足的Nevanlinna条件，并给出极值性的一般算子理论判据。随后，我们推导出两个变量中实有理Herglotz-Nevanlinna函数的表示测度的显式公式，并将其与极值性判据相结合，从而在Nevanlinna测度的全锥中获得一族极值元素。该族包含具有可约分母的例子，这些例子构成了Knese猜想中不可约性断言的反对例。最后，我们在该族内从代数和几何两个角度刻画了可约性。
英文摘要
We first revisit the Nevanlinna condition for representing measures of Herglotz-Nevanlinna functions in two variables and give a general operator-theoretic criterion for extremality. We then derive an explicit formula for the representing measure of a real rational Herglotz-Nevanlinna function in two variables, and combine it with the extremality criterion to obtain a family of extreme elements in the full cone of Nevanlinna measures. The family includes examples with reducible denominators, and these yield counterexamples to the irreducibility assertion in a conjecture of Knese. We then characterize reducibility within this family both algebraically and geometrically.
发表机构
- Stockholm University（斯德哥尔摩大学）
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