偶数阶自共轭微分算子谱的离散性条件  

The conditions for the discreteness of the spectrum of self-adjoint differential operators of even order

作　　者：索建青[1] 王万义[1] 

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《中国科学：数学》2013年第5期489-497,共9页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:10961019);内蒙古大学高层次人才引进科研项目(批准号:125131)资助项目

摘　　要：本文主要研究2n阶对称微分算式a[u]=n∑k=0(1)k(ak(x)u(k)(x))(k),x∈(0,∞)所生成的微分算子谱的离散性条件,首先得出当系数ak(x)由ex的幂所控制时,其谱是离散的结论;其次得到当x→∞时,系数ak(x)可能随着ex的幂增大而增大,其谱是离散的充分与必要条件.In this paper, we consider differential operators of 2nd-order a[u]=k=0∑n（-1）^k（ak（x）u^（k）（x））^（k）,x∈（0,∞）whose coefficients ak （x） are restricted by powers of e^x, and give conditions on the coefficients sufficient to ensure that the spectrum is discrete; next we formulate necessary and sufficient conditions for the discreteness of the spectrum of differential operators whose coefficients ak （x） may increase as e^akz as x → ∞.

关 键 词：自共轭微分算子 本质谱 离散谱 

分 类 号：O175.3[理学—数学]