Heine-Stieltjes定理的推广
A generalization of the Heine--Stieltjes theorem
摘要：
本文将Heine-Stieltjes定理推广到所有保持只有实零点的非退化微分算子。这解决了B的一个猜想。夏皮罗开发的新方法被用来描述复杂的交织关系的零不同对的解决方案。这扩展了Bourget，McMillen和Vargas关于Heun方程的最近结果，并回答了他们关于如何将结果推广到更高程度的问题。许多结果是新的，即使是经典的情况下。
英文摘要：
We extend the Heine-Stieltjes Theorem to concern all (non-degenerate) differential operators preserving the property of having only real zeros. This solves a conjecture of B. Shapiro. The new methods developed are used to describe intricate interlacing relations between the zeros of different pairs of solutions. This extends recent results of Bourget, McMillen and Vargas for the Heun equation and answers their question on how to generalize their results to higher degrees. Many of the results are new even for the classical case.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
