四阶正则微分算子耦合自共轭边界条件的基本标准型

Canonical Forms of Coupled Self-adjoint Boundary Conditions for Regular Differential Operators of Order Four

本文利用新的方法给出了4阶正则微分算子耦合自共轭边界条件的基本标准型,新标准型中的4个分块小矩阵为对称矩阵,且其行列式的模为1.这与2阶微分算子耦合边界条件的标准型极为类似,这为给出一般的高阶微分算子自共轭边界条件标准型提供了新的思路.

We present the canonical forms of coupled self-adjoint boundary conditions for regular differential operators of order four by using new methods. In this new canonical forms, the four small block matrices are symmetric, and the determinant has absolute value equal to 1. This fourth order form is quite similar to the new second order one, and it provides a new way to give the canonical forms of the self-adjoint boundary condition for general high-order differential operators.