逆谱理论新方法中A-函数和势函数依赖关系的稳定性研究  

An Research in the Stability of the Dependence between the Potential and the A-function Introduced in the New Approach to Inverse Spectral Theory

作　　者：李丽[1] 黄振友[2] 

机构地区：[1]黄山学院数学系,黄山245041 [2]南京理工大学数学系,南京210094

出　　处：《应用数学学报》2012年第4期577-585,共9页Acta Mathematicae Applicatae Sinica

基　　金：黄山学院科研项目(2010xkj015)资助

摘　　要：对于一维Schrdinger算子,本文基于Simon给出的惟—性定理(势函数由A-函数惟一确定)证明了势函数连续依赖于A-函数;反过来,若势函数q∈L^1(0,∞),给出了A-函数也连续依赖于势函数的结论.In this paper, for one dimensional SchSdinger operator, we prove that the po- tential is continuous dependent on the A-function based on Simon＇s uniqueness theorem （the potential is determined by A-function uniquely）; conversely, if the potential q ∈ L1 （0, ∞）, it is concluded that the A-function is also continuous dependent on the potential.

关 键 词：Schrdinger算子 逆谱 A-函数 势函数 连续依赖性 

分 类 号：O177.7[理学—数学]