论文标题
反频谱问题的均匀稳定性，用于卷积全差异操作员
Uniform stability of the inverse spectral problem for a convolution integro-differential operator
论文作者
论文摘要
双重分化的操作员被分化操作员的组成和一个卷积的卷积扰动，在有限的间隔内与Dirichlet边界条件的有限间隔一样。我们获得统一的稳定性，可以从加权$ l_2 $ norm和加权统一规范中从光谱中恢复卷积内核。为此，我们依次证明了算法的每个步骤的统一稳定性，用于解决这两个规范中的反向问题。除了证明数值计算的合理性外，获得的结果还显示出与经典逆变符号问题的必要区别。
The operator of double differentiation, perturbed by the composition of the differentiation operator and a convolution one, on a finite interval with Dirichlet boundary conditions is considered. We obtain uniform stability of recovering the convolution kernel from the spectrum in a weighted $L_2$-norm and in a weighted uniform norm. For this purpose, we successively prove uniform stability of each step of the algorithm for solving this inverse problem in both the norms. Besides justifying the numerical computations, the obtained results reveal some essential difference from the classical inverse Sturm-Liouville problem.
