An inverse problem for the Dirac system on the semiaxis, with discrete spectrum

1987 ◽  
pp. 43-47
Author(s):  
T. N. Arutyuyan
Keyword(s):  
Inverse Problem ◽  
Discrete Spectrum ◽  
Dirac System

Reply to Comment on 'Inverse problem from the discrete spectrum in the D = 2 dimensional space'

2022 ◽  
Author(s):  
Roland Lombard ◽  
Rabia Yekken
Keyword(s):  
Inverse Problem ◽  
Discrete Spectrum ◽  
Dimensional Space

Abstract We want to thank our colleague F. Fernandez for his interest and his careful reading of our paper "The inverse problem from discrete spectrum in the D = 2 dimensional space". We are confused to have left a number of mistakes in the manuscript.

Inverse problem for a one-dimensional dynamical Dirac system (BC-method)

2014 ◽  
Vol 30 (12) ◽  
pp. 125013 ◽  
Author(s):  
M I Belishev ◽  
V S Mikhailov
Keyword(s):  
Inverse Problem ◽  
Dirac System ◽  
One Dimensional

The inverse scattering problem for a discrete dirac system on the whole axis

2017 ◽  
Vol 25 (6) ◽  
Author(s):  
Hidayat M. Huseynov ◽  
Agil K. Khanmamedov ◽  
Rza I. Aleskerov
Keyword(s):  
Inverse Problem ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Scattering Data ◽  
Sufficient Condition ◽  
Dirac System ◽  
Entire Line

AbstractThis paper investigates the inverse scattering problem for a discrete Dirac system on the entire line with coefficients that stabilize to zero in one direction. We develop an algorithm for solving the inverse problem of reconstruction of coefficients. We derive a necessary and a sufficient condition on the scattering data so that the inverse problem is uniquely solvable.

scholarly journals An inverse problem for the integro-differential Dirac system with partial information given on the convolution kernel

2019 ◽  
Vol 27 (2) ◽  
pp. 151-157 ◽  
Author(s):  
Natalia Pavlovna Bondarenko
Keyword(s):  
Inverse Problem ◽  
Uniqueness Theorem ◽  
Partial Information ◽  
A Priori ◽  
Sufficient Conditions ◽  
Convolution Kernel ◽  
Dirac System ◽  
Integral Term ◽  
Necessary And Sufficient ◽  
The Uniqueness Theorem

AbstractAn integro-differential Dirac system with an integral term in the form of convolution is considered. We suppose that the convolution kernel is known a priori on a part of the interval, and recover it on the remaining part, using a part of the spectrum. We prove the uniqueness theorem, provide an algorithm for the solution of the inverse problem together with necessary and sufficient conditions for its solvability.

scholarly journals Discrete spectrum of perturbed Dirac systems with real and periodic coefficients

1990 ◽  
Vol 115 (3-4) ◽  
pp. 337-347
Author(s):  
Boris Buffoni
Keyword(s):  
Discrete Spectrum ◽  
Upper Bound ◽  
Dirac System ◽  
Periodic Coefficients ◽  
Dirac Systems

SynopsisThis paper deals with the number of eigenvalues which appear in the gaps of the spectrum of a Dirac system with real and periodic coefficients when the coefficients are perturbed. The main results provide an upper bound and a condition under which exactly one eigenvalue appears in a given gap.

scholarly journals Direct and Inverse Spectral Problems for Rank-One Perturbations of Self-adjoint Operators

2021 ◽  
Vol 93 (2) ◽  
Author(s):  
Oles Dobosevych ◽  
Rostyslav Hryniv
Keyword(s):  
Inverse Problem ◽  
Discrete Spectrum ◽  
Adjoint Operator ◽  
Inverse Spectral Problems ◽  
Spectral Problems ◽  
Rank One ◽  
Inverse Spectral ◽  
Adjoint Operators

AbstractFor a given self-adjoint operator A with discrete spectrum, we completely characterise possible eigenvalues of its rank-one perturbations B and discuss the inverse problem of reconstructing B from its spectrum.

Sign in / Sign up

Export Citation Format

Share Document