CAJ | 학술논문

本文讨论边界条件中含有谱参数的Sturm-Liouville算子的逆问题，并且建立了这个算子的惟一性定理．利用Hochstadt-Lieberman的方法及整函数的性质，我们证明对固定的非负整数n，如果测得一组不同参数边界条件下Sturm-Liouville算子的第n个特征值的无穷集合，则组谱集合能够惟一确定区间[0,π]上的势函数q(x)及边界条件中的系数h．
본문토론변계조건중함유보삼수적Sturm-Liouville산자적역문제，병차건립료저개산자적유일성정리．이용Hochstadt-Lieberman적방법급정함수적성질，아문증명대고정적비부정수n，여과측득일조불동삼수변계조건하Sturm-Liouville산자적제n개특정치적무궁집합，칙조보집합능구유일학정구간[0,π]상적세함수q(x)급변계조건중적계수h．
The inverse problem of Sturm-Liouville operators with boundary condition depen-dent on the spectral parameter is considered and a uniqueness theorem for the Sturm-Liouville operator is established in this paper. Applying the Hochstadt-Lieberman’s method and prop-erties of entire functions, we verify that if the infinite set of the n-th eigenvalues for the Sturm-Liouville operator of the different boundary conditions can be measured for a fixed non-negative integer n, then this spectral set is sufficient to determine the potential q(x) on the interval [0,π] and the coefficient h of the boundary condition.