有理椭圆系数差分方程的解析理论与Riemann-Hilbert问题
Analytic theory of difference equations with rational and elliptic coefficients and the Riemann-Hilbert problem
摘要：
提出了一种新的有理椭圆系数差分方程解析理论的方法。它是基于构造的典型亚纯解，这是解析沿“厚路径”。这种解决方案的概念导致了差分方程的局部monodromies的概念。证明了在连续极限下，它们收敛于微分方程的单值矩阵。构造了椭圆系数差分方程的一类新的改变椭圆曲线周期的等距单点变形。
英文摘要：
A new approach to the analytic theory of difference equations with rational and elliptic coefficients is proposed. It is based on the construction of canonical meromorphic solutions which are analytical along "thick paths". The concept of such solutions leads to a notion of local monodromies of difference equations. It is shown that in the continuous limit they converge to the monodromy matrices of differential equations. New type of isomonodromic deformations of difference equations with elliptic coefficients changing the periods of elliptic curves is constructed.
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。
