Real-root property of the spectral polynomial of the Treibich–Verdier potential and related problems

Zhijie Chen, Ting Jung Kuo, Chang Shou Lin, Kouichi Takemura

研究成果: 雜誌貢獻文章

3 引文 斯高帕斯(Scopus)

摘要

We study the spectral polynomial of the Treibich–Verdier potential. Such spectral polynomial, which is a generalization of the classical Lamé polynomial, plays fundamental roles in both the finite-gap theory and the ODE theory of Heun's equation. In this paper, we prove that all the roots of such spectral polynomial are real and distinct under some assumptions. The proof uses the classical concept of Sturm sequence and isomonodromic theories. We also prove an analogous result for a polynomial associated with a generalized Lamé equation, where we apply a new approach based on the viewpoint of the monodromy data.

原文英語
頁(從 - 到)5408-5431
頁數24
期刊Journal of Differential Equations
264
發行號8
DOIs
出版狀態已發佈 - 2018 四月 15

    指紋

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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