Archimedean Spiral上矩阵值边值问题

Matrix Valued Boundary Value Problem on Archimedean Spiral

摘要: 研究阿基米德螺线上的一类特殊的下三角矩阵值边值问题。首先使用双线性形式给出阿基米德螺线上的伪正交多项式并说明这是唯一存在的；其次给出特殊的下三角矩阵值边值问题并转化为四组有联系的边值问题；最后使用Liouville定理和Painlevé定理以及伪正交多项式给出解。

Abstract: This paper studies a special kind of lower triangular matrix value boundary value problem on Archimedeanspiral. First, the pseudo-orthogonal polynomial on the Archimedeanspiral is given in bilinear form and shows that it exists only; Secondly, the special lower triangular matrix value boundary value problem is given and transformed into four groups of related boundary value problems; Finally, the solution is given by using Liouville theorem and Painlevé theorem and pseudo-orthogonal polynomials.