一类具有离散谱的对称微分算子  

A CLASS OF SYMMETRIC DIFFERENTIAL OPERATORS WITH DISCRETE SPECTRUM

作　　者：杨瑞芳[1] 

机构地区：[1]南京航空航天大学理学院,南京210016

出　　处：《系统科学与数学》2000年第4期417-423,共7页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金资助课题

摘　　要：研究了一类２ｎ－阶线性微分算子在加权Ｈｉｌｂｅｒｔ空间中的谱．通过对加权Ｓｏｂｏｌｅｖ空间Ｈ２ｎ紧嵌入到加权 Ｌ２空间 Ｌｒ３中的讨论，给出了线性算子的本质谱的存在区间，特别是当其系数满足一定条件时，它的谱是离散的．The investigation deals with the spectrum of a class of differential operators of order 2n where the underlying Hilbert space is weighted. The author considers the embedding problem of the weighted Sobolev space H2n into the weighted L2 space Lr2. Using the results obtained,we give the existence interval for the essential spectrum. Especiallys conditions on the coefficients are given such that the spectra are discrete.

关 键 词：加权HIBERT空间 谱理论 线性微分算子 对称微分算子 

分 类 号：O175.3[理学—数学]