scholarly journals On an inverse eigenvalue problem for a semilinear Sturm–Liouville operator

2008 ◽  
Vol 68 (3) ◽  
pp. 639-644 ◽  
Author(s):  
Peter Zhidkov
Keyword(s):  
Eigenvalue Problem ◽  
Liouville Operator ◽  
Inverse Eigenvalue Problem ◽  
Inverse Eigenvalue ◽  
Sturm Liouville

scholarly journals Inverse Eigenvalue Problems for Singular Rank One Perturbations of a Sturm-Liouville Operator

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Xuewen Wu
Keyword(s):  
Eigenvalue Problem ◽  
Potential Function ◽  
Liouville Operator ◽  
Eigenvalue Problems ◽  
Inverse Eigenvalue Problem ◽  
Inverse Eigenvalue Problems ◽  
Rank One ◽  
Inverse Eigenvalue ◽  
Sturm Liouville

This paper is concerned with the inverse eigenvalue problem for singular rank one perturbations of a Sturm-Liouville operator. We determine uniquely the potential function from the spectra of the Sturm-Liouville operator and its rank one perturbations.

scholarly journals Toeplitz nonnegative realization of spectra via companion matrices

2019 ◽  
Vol 7 (1) ◽  
pp. 230-245
Author(s):  
Macarena Collao ◽  
Mario Salas ◽  
Ricardo L. Soto
Keyword(s):  
Eigenvalue Problem ◽  
Half Plane ◽  
Toeplitz Matrix ◽  
Toeplitz Matrices ◽  
Nonnegative Matrix ◽  
Inverse Eigenvalue Problem ◽  
Complex Numbers ◽  
Inverse Eigenvalue ◽  
Companion Matrices ◽  
Solution Matrix

Abstract The nonnegative inverse eigenvalue problem (NIEP) is the problem of finding conditions for the existence of an n × n entrywise nonnegative matrix A with prescribed spectrum Λ = {λ1, . . ., λn}. If the problem has a solution, we say that Λ is realizable and that A is a realizing matrix. In this paper we consider the NIEP for a Toeplitz realizing matrix A, and as far as we know, this is the first work which addresses the Toeplitz nonnegative realization of spectra. We show that nonnegative companion matrices are similar to nonnegative Toeplitz ones. We note that, as a consequence, a realizable list Λ= {λ1, . . ., λn} of complex numbers in the left-half plane, that is, with Re λi≤ 0, i = 2, . . ., n, is in particular realizable by a Toeplitz matrix. Moreover, we show how to construct symmetric nonnegative block Toeplitz matrices with prescribed spectrum and we explore the universal realizability of lists, which are realizable by this kind of matrices. We also propose a Matlab Toeplitz routine to compute a Toeplitz solution matrix.

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