周期边界条件下Sturm-Liouville方程组特征值问题的迹公式

Trace Formula for the Eigenvalue Problem of Sturm-Liouville Equation System with Periodic Boundary Condition

讨论了周期边界条件下Sturm-Liouville方程组特征值问题.首先将特征值的存在性问题化为一个整函数零点的存在性问题,然后借助于一个积分恒等式,采用留数方法,得到了周期边界条件下Sturm-Liouville方程组特征值问题的迹公式.

The eigenvalue problem of Sturm-Liouville equation system with periodic boundary condition is discussed. The eigenvalue problem is turned into the zero problem of an entire function. By the integral identity and residue method, the trace formula for the above eigenvalue problem of Sturm-Liouville system is obtained.