复系数2n阶微分算子的谱

The Spectrum of 2nth Order Differential Operators with Complex Coefficients

本文研究了复系数２ｎ阶微分算式（２．１）生成的Ｊ－自伴微分算子谱，对两类微分算子的本质谱，离散谱作了定性研究，得到了所生成微分算子本质谱的存在范围，以及所生成微分算子的谱是离散的充分条件．

In this paper, we discussed the spectrum of J-selfadjoint operators that are extended by 2nth order differential expressions (2.1) with complex coefficients. We obtained that the essential spectrum of J-selfadjoint operators is contained in the set A when the coefficients of (2.1) satisfied conditions in theorem 3.2. Finally we gave some sufficient conditions for the discreteness spectrum of J-selfadjoint operators that are extended by (2.1) and Sturm-Liouville differential operations with complex coefficients.