具有Robin边界条件的Schrodinger算子传输特征值密度  

On the Density of Transmission Eigenvalue for the Schrodinger Operator with the Robin Boundary Condition

作　　者：马利杰 徐小川 Li Jie MA;Xiao Chuan XU(School of Mathematicsand Statistics,Nanjing University of Information Scienceand Technology,Nanjing 210044,P.R.China)

机构地区：[1]南京信息工程大学数学与统计学院,南京210044

出　　处：《数学学报（中文版）》2022年第6期959-966,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11901304)。

摘　　要：本文研究具有Robin边界条件的传输特征值问题,运用指数型整函数的相关性质刻画特征值密度与势函数支撑区间长度的关系.同时,证明传输特征值问题等价于一类边界条件带有谱参数的Sturm-Liouville问题.In this paper,we study the transmission eigenvalue problem with the Robin boundary condition.Applying the related properties of entire function of exponential type,we show the relationship between the density of eigenvalues and the length of the support interval of the potential function.Meanwhile,we prove that the transmission eigenvalue problem is equivalent to a kind of Sturm-Liouville problem with spectral parameter in the boundary condition.

关 键 词：传输特征值 零点密度 指数型整函数 指示函数 STURM-LIOUVILLE问题 

分 类 号：O175.7[理学—数学]