【摘要】 研究了一类内部具有无穷多个不连续点的Sturm Liouville问题,即内部具有无穷多个转移条件的Sturm Liouville问题.首先建立了新Hilbert空间,在新的空间中定义了与转移条件相关联的最小算子C_min和最大算子C_max,并给出了它们的性质.之后利用算子分解法得到了最小算子C_min自共轭扩张谱是离散的充分条件.更多还原

【Abstract】 In this paper,we study a class of Sturm Liouville problems with an infinite number of interior discontinuous points,i.e.,Sturm Liouville problems with an infinite number of transmission conditions at interior points.Firstly,we construct a new Hilbert space associated with the transmission conditions and define the maximal and minimal operators C_max,C_minassociated with the transmission conditions in the new Hilbert space,and give some properties of the operators C_max,C_min.And then we obtain a sufficient condition which ensure that the spectrum of the self-adjoint operators of the operator C_min is discrete by using the operator decomposition method.更多还原