指数函数曲线上的矩阵值Riemann边值问题

Matrix Value Riemann Boundary Value Problems on the Exponential Function Curve

摘要: 本文讨论的是指数函数曲线上的矩阵值Riemann边值问题，我们主要是对一类特殊的下三角矩阵值Riemann边值问题进行求解。首先使用双线性形式给出指数函数曲线上的伪正交多项式；其次给出特殊的下三角矩阵值边值问题并转化为边值问题；最后使用Liouville定理和伪正交多项式给出矩阵值Riemann边值问题的求解。

Abstract: In this paper, we mainly discussed matrix value Riemann boundary value problems on the expo-nential function curve and solved a special class of lower triangular matrix value Riemann boundary value problems. Firstly, the pseudo-orthogonal polynomial on the curve of exponential function is given by using bilinear form. Secondly, a special boundary value problem of lower tri-angular matrix values is presented and transformed into a boundary value problem. Finally, the solution of Riemann boundary value problem with matrix values is given by Liouville theorem and pseudo-orthogonal polynomials.