参数边界条件下Sturm-Liouville算子的逆谱问题  

Inverse Spectral Problems for Sturm-Liouville Operators with Boundary Conditions Dependent on the Spectral Parameter

作　　者：王於平[1] WANG Yuping(Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China)

机构地区：[1]南京林业大学应用数学系,南京210037

出　　处：《应用泛函分析学报》2017年第3期294-298,共5页Acta Analysis Functionalis Applicata

摘　　要：本文研究参数边界条件下Sturm-Liouville算子的逆谱问题.利用Weyl函数的结果,证明对固定的n,n∈N_0,及不同的b_k,谱集合{λ_n(q,b_k)}_(k=1)^(+∞)能够唯一确定[0,1]上的势函数q(x),这个定理是文献[4]结果的本质推广.Abstract In this paper, we discuss the inverse spectral problem for Sturm-Liouville operators with boundary conditions dependent on the spectral parameter. For each fixed n, n ∈N0and various real number bk, we show that the spectral set {λn（q,bk）}＋∞k=1 is sufficient to determine the potential q（x） on [0, 1] by the known result on the Weyl function, which is a generalization of the result in Ref [4].

关 键 词：逆谱问题 边值问题 参数边界条件 势函数 

分 类 号：O175.3[理学—数学]