Inverse spectral problem for Jacobi matrices with partial spectral data

2011 ◽  
Vol 27 (7) ◽  
pp. 075007 ◽  
Author(s):  
Guangsheng Wei ◽  
Zhaoying Wei
Keyword(s):  
Spectral Problem ◽  
Spectral Data ◽  
Inverse Spectral Problem ◽  
Jacobi Matrices ◽  
Inverse Spectral

scholarly journals An inverse spectral problem for a star graph of Krein strings

2016 ◽  
Vol 2016 (715) ◽  
Author(s):  
Jonathan Eckhardt
Keyword(s):  
Spectral Problem ◽  
Spectral Data ◽  
Inverse Spectral Problem ◽  
Trace Class ◽  
Star Graph ◽  
Borel Measures ◽  
Inverse Spectral ◽  
The Individual

AbstractWe solve an inverse spectral problem for a star graph of Krein strings, where the known spectral data comprises the spectrum associated with the whole graph, the spectra associated with the individual edges as well as so-called coupling matrices. In particular, we show that these spectral quantities uniquely determine the weight within the class of Borel measures on the graph, which give rise to trace class resolvents. Furthermore, we obtain a concise characterization of all possible spectral data for this class of weights.

scholarly journals On a Discrete Inverse Problem for Two Spectra

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Gusein Sh. Guseinov
Keyword(s):  
Inverse Problem ◽  
Spectral Problem ◽  
Finite Order ◽  
Inverse Spectral Problem ◽  
Jacobi Matrix ◽  
Jacobi Matrices ◽  
Symmetric Matrices ◽  
The Matrix ◽  
Inverse Spectral

A version of the inverse spectral problem for two spectra of finite-order real Jacobi matrices (tridiagonal symmetric matrices) is investigated. 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 deleting the last row and last column of the Jacobi matrix.

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