\(m\)-functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices. (English) Zbl 0924.15005
The inverse spectral problem for finite and infinite Jacobi matrices \(H\) is treated. A new proof using \(m\)-functions of the central result, namely that the spectral measure determines \(H\) uniquely, is given. Also it is shown, that the \(N\times N\)-Jacobi matrix \(H\) is determined by any \(j\) eigenvalues and \(c_{j+1},\dots,c_{2N-1}\), where the \(c_1,c_3,c_5,\dots\) are the diagonal entries and \(c_2,c_4,c_6,\dots\) are the non-diagonal entries of \(H\). This generalizes a result of Hochstadt, who had treated the case \(j=N\).
Reviewer: L.Elsner (Bielefeld)
MSC:
| 15A18 | Eigenvalues, singular values, and eigenvectors |
Keywords:
inverse eigenvalue problem; finite Jacobi matrices; infinite Jacobi matrices; \(m\)-functions; spectral measureReferences:
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