On an inverse problem for two spectra of finite Jacobi matrices

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• 作者：Gusein Sh. Guseinov ^{guseinov@atilim.edu.tr}
• 关键词：Jacobi matrix ; Difference equation ; Spectrum ; Normalizing number ; Inverse problem
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 期刊代码：7_00963003
• 类别：cp
• 出版时间：15 March, 2012
• 卷：218
• 期：14
• 页码：7573-7589
• 文件大小：309 K

摘要

We solve a version of the inverse spectral problem for two spectra of finite order real Jacobi matrices. The problem is to reconstruct the matrix using two sets of eigenvalues, one for the original Jacobi matrix and one for the matrix obtained by replacing the last diagonal element of the Jacobi matrix by some another number. The uniqueness and existence results for solution of the inverse problem are established and an explicit procedure of reconstruction of the matrix from the two spectra is given.