一类奇异自伴微分算子的本质谱

On the Essential Spectrum of a Class of Singular Self-adjoint Differential Operators

考虑一类微分算式中具有对数函数系数的自伴微分算子,并主要通过构造奇异序列的方法得到了一定条件下算子的本质谱.与Euler微分算子的本质谱进行比较,可见对数函数系数对算子的谱产生了很大影响.

We considered a class of self-adjoint differential operators with logarithmic coefficients in the expressions,and got the essential spectrum of the operators under certain conditions by constructing singular sequences.The comparison of the essential spectrum of the operators concerned with that of the Euler differential operators showed that the logarithmic coefficients had a remarkable effect on the spectrum of the operators.