2n阶J-自伴算子的豫解算子及其谱分析

Resolvent Operator and Spectrum Analysis of the 2n-order J-self-adjoint Operator

基于具有可积复系数函数的2n阶线性微分方程解的渐近式,讨论了复系数2n阶微分方程平方可积解的个数与其最小算子的亏指数,再利用2n阶J-自伴算子的豫解算子的性质,研究2n阶J-自伴算子的谱,得出了一个与实系数情形类似的重要结论。

Based on the asymptotic expression of the solution of 2n order linear differential equation who has integrable plural coefficients functions, the number of square integrable solutions and the deficiency index of the minimum operator of 2n order differential equation with complex coeflleients are discussed. Then, the properties of the resolvent operators are used to study the spectrum of the 2n-order J- self-adjoint differential operator. An important conclusion that the property is similar to that of the real coefficients J- symmetric differential operator is obtained.