利用算子直和分解的方法和二次型比较的方法, 研究一类$2n(n\ge 1)$阶微分算子谱的离散性, 得到该微分算子的谱是离散的几个充分必要条件.

The discreteness of the spectrum of a class of $2n$ order differential operators  is discussed. Some necessary and sufficient conditions for the discreteness of   the spectra of the considered operators are obtained with direct sum decomposition method of operators and estimation of the corresponding quadratic forms.