کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8898861 | 1631502 | 2018 | 24 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Real-root property of the spectral polynomial of the Treibich-Verdier potential and related problems
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 264, Issue 8, 15 April 2018, Pages 5408-5431
Journal: Journal of Differential Equations - Volume 264, Issue 8, 15 April 2018, Pages 5408-5431
نویسندگان
Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin, Kouichi Takemura,