具有算子系数的微分算子新的Ambarzumyan定理(英文)  

New Ambarzumyan's Theorems for Differential Operators With Operator Coefficient

作　　者：杨传富[1] 王丰[1] 

机构地区：[1]南京理工大学应用数学系,南京江苏210094

出　　处：《数学进展》2011年第6期749-755,共7页Advances in Mathematics（China）

基　　金：supported by NSFC(No11171152);Natural Science Foundation of Jiangsu Province of China(NoBK 2010489);the Outstanding Plan-Zijin Star Foundation of NUST(NoAB 41366);NUST Research Funding(NoAE 88787)

摘　　要：有限区间上具有Neumann边界条件的Sturm-Liouville问题的谱可以唯一确定势函数,这就是经典的Ambarzumyan定理.本文将经典的Ambarzumyan定理推广到有限区间上具有算子系数的二阶与四阶微分算子中.Ambarzumyan＇s theorem describes the exceptional case in which the spectrum of a single Sturm-Liouville problem with the Neumann boundary conditions on a finite interval uniquely determines the potential. In this paper, the result of Ambarzumyan is extended to second order and fourth order differential operators with operator coefficient in a finite interval.

关 键 词：逆谱问题 Ambarzumyan型定理 算子系数微分算子 

分 类 号：O175.3[理学—数学]