2×2 Sturm-Liouville问题特征函数系的完备性

The completeness of eigenvalue functions of the 2×2 Sturm-Liouvill's problem

研究了一个2×2SturmLiouville问题,证明了与它相联系的积分算子为全连续算子,从而得到了2×2SturmLiouville问题特征函数系的完备性以及二元向量按其展开的特征展开定理.

In this paper , the 2 × 2 Sturm -Liouvill＇s problem is discussed. The integral operator associated withthe 2 × 2 Sturm - Liouvill＇s problem is proved to be a completely continuous operator. Meanwhile the completeness of eigenvalue functions of this operator and eigenvalue expansion theorem are also obtained.