复系数2n阶微分算子的谱  

The Spectrum of 2nth Order Differential Operators with Complex Coefficients

作　　者：王忠 

机构地区：[1]西江大学数学与计算机系,广东肇庆526061

出　　处：《数学学报（中文版）》2000年第5期787-796,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金!(19871037); 内蒙自然科学基金

摘　　要：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.

关 键 词：J-自伴微分算子 本质谱 离散谱 复系数 2n阶微分算子 

分 类 号：O175.3[理学—数学]