一类具有幂指积系数的微分算子的离散谱

The discrete spectrum of a class of differential operators with product of power function and exponential function

利用算子的直和分解原理及二次型比较的方法研究了一类系数中含有幂函数与指数函数乘积的2n阶实系数微分算子谱的离散性.给出了其谱是离散的一些充分条件.利用这些充分条件可以判别微分算子谱的离散性.

Using the method of direct sum decomposition and estimation of the corresponding quadratic forms,the discrete spectrum of a class of 2n-th order differential operators are considered,whose coefficients contain product of power function and exponential function. Some sufficient conditions are given which ensure that the spectrum of differential operators is discrete. And the discreteness of spectrum of some differential operators can be easily judged.