Inverse problems for Jacobi operators: I. Interior mass–spring perturbations in finite systems
Inverse problems for Jacobi operators: I. Interior mass–spring perturbations in finite systems
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雅可比算子的逆问题：I. 有限系统中的内部质量-弹簧扰动
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
M. Kudryavtsev
中科院分区：
文献类型：
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作者：
R. Del Río;M. Kudryavtsev
我们考虑一个线性有限弹簧-质量系统，它通过修改一个质量和增加一个弹簧来摄动。我们研究质量和弹簧何时可以从原始系统和扰动系统的自然频率中恢复。这是一个关于有限雅可比矩阵的秩2或秩3扰动的问题，其中我们能够非常明确地描述相关的格林函数。给出了两个给定点集分别是原系统和修正系统的特征值的充要条件。
We consider a linear finite spring–mass system which is perturbed by modifying one mass and adding one spring. We study when masses and springs can be recovered from the natural frequencies of the original and the perturbed systems. This is a problem about rank 2 or rank 3 perturbations of finite Jacobi matrices where we are able to describe quite explicitly the associated Green’s functions. We give necessary and sufficient conditions for two given sets of points to be eigenvalues of the original and modified systems, respectively.