scholarly journals Direct and inverse spectral problems for Dirac systems with nonlocal potentials

2019 ◽  
Vol 39 (5) ◽  
pp. 645-673
Author(s):  
Kamila Dębowska ◽  
Leonid P. Nizhnik
Keyword(s):  
Characteristic Function ◽  
Dirac System ◽  
Inverse Spectral Problems ◽  
One Dimensional ◽  
Spectral Problems ◽  
Dirac Systems ◽  
Inverse Spectral ◽  
The One ◽  
The Given ◽  
Nonlocal Potentials

The main purposes of this paper are to study the direct and inverse spectral problems of the one-dimensional Dirac operators with nonlocal potentials. Based on informations about the spectrum of the operator, we find the potential and recover the form of the Dirac system. The methods used allow us to reduce the situation to the one-dimensional case. In accordance with the given assumptions and conditions we consider problems in a specific way. We describe the spectrum, the resolvent, the characteristic function etc. Illustrative examples are also given.

scholarly journals Inverse dynamic and spectral problems for the one-dimensional Dirac system on a finite tree

2018 ◽  
Vol 26 (5) ◽  
pp. 673-680
Author(s):  
Alexander Mikhaylov ◽  
Victor S. Mikhaylov ◽  
Gulden Murzabekova
Keyword(s):  
Dynamic Response ◽  
Matrix Function ◽  
Dirac System ◽  
Inverse Dynamic ◽  
Finite Tree ◽  
Response Operator ◽  
One Dimensional ◽  
Spectral Problems ◽  
The Matrix ◽  
The One

Abstract We consider inverse dynamic and spectral problems for the one-dimensional Dirac system on a finite tree. Our aim will be to recover the topology of a tree (lengths and connectivity of edges) as well as the matrix potentials on each edge. As inverse data we use the Weyl–Titchmarsh matrix function or the dynamic response operator.

scholarly journals Determination of differential pencils with impulse from interior spectral data

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yongxia Guo ◽  
Guangsheng Wei ◽  
Ruoxia Yao
Keyword(s):  
Spectral Data ◽  
Interior Point ◽  
Potential Functions ◽  
Inverse Spectral Problems ◽  
Spectral Problems ◽  
Inverse Spectral ◽  
Differential Pencils ◽  
Second Spectrum

Abstract In this paper, we are concerned with the inverse spectral problems for differential pencils defined on $[0,\pi ]$ [ 0 , π ] with an interior discontinuity. We prove that two potential functions are determined uniquely by one spectrum and a set of values of eigenfunctions at some interior point $b\in (0,\pi )$ b ∈ ( 0 , π ) in the situation of $b=\pi /2$ b = π / 2 and $b\neq \pi /2$ b ≠ π / 2 . For the latter, we need the knowledge of a part of the second spectrum.

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