Erratum: Recovery of the Dirac system from the rectangular Weyl matrix function

2012 ◽  
Vol 28 (2) ◽  
pp. 029601
Author(s):  
B Fritzsche ◽  
B Kirstein ◽  
I Ya Roitberg ◽  
A L Sakhnovich
Keyword(s):  
Matrix Function ◽  
Dirac System ◽  
Weyl Matrix

scholarly journals Recovery of the Dirac system from the rectangular Weyl matrix function

2011 ◽  
Vol 28 (1) ◽  
pp. 015010 ◽  
Author(s):  
B Fritzsche ◽  
B Kirstein ◽  
I Ya Roitberg ◽  
A L Sakhnovich
Keyword(s):  
Matrix Function ◽  
Dirac System ◽  
Weyl Matrix

A Titchmarsh-Weyl matrix function for symmetric differential equations of order 2n with an indefinite weight function

1984 ◽  
Vol 98 (3-4) ◽  
pp. 311-337
Author(s):  
Karim Daho
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Weight Function ◽  
Matrix Function ◽  
Present Author ◽  
Krein Space ◽  
Indefinite Weight ◽  
Weyl Matrix ◽  
Indefinite Weight Function ◽  
Image Position

SynopsisA Titchmarsh-Weyl matrix function W(λ) is defined for the differential equation of order 2nwith po>0, pk≧0, k = 1, 2, …, n on 005B;0, b), λєℂ and an indefinite weight function r. It is shown that this function W(λ) belongs to some class and that some operators associated with the above equation are definitizable in the Krein space . In the particular case n = 1, these results are contained in an earlier paper by the present author and H. Langer.

An estimate of the Cauchy matrix function for the dirac system in the case of finite-gap nonperiodic potentials

1993 ◽  
Vol 53 (4) ◽  
pp. 400-409 ◽  
Author(s):  
B. M. Levitan ◽  
A. �. Mamatov
Keyword(s):  
Matrix Function ◽  
Dirac System ◽  
Cauchy Matrix

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 Inverse problems for Aharonov–Bohm rings

2009 ◽  
Vol 148 (2) ◽  
pp. 331-362 ◽  
Author(s):  
P. KURASOV
Keyword(s):  
Magnetic Field ◽  
Inverse Problem ◽  
Matrix Function ◽  
Characteristic Zero ◽  
Resonance Condition ◽  
Metric Graphs ◽  
Weyl Matrix ◽  
Dirichlet To Neumann Map ◽  
Aharonov Bohm ◽  
The Magnetic Field

AbstractThe inverse problem for Schrödinger operators on metric graphs is investigated in the presence of magnetic field. Graphs without loops and with Euler characteristic zero are considered. It is shown that the knowledge of the Titchmarsh–Weyl matrix function (Dirichlet-to-Neumann map) for just two values of the magnetic field allows one to reconstruct the graph and potential on it provided a certain additional no-resonance condition is satisfied.

scholarly journals NONCOMMUTATIVE GRAPHENE

2013 ◽  
Vol 28 (16) ◽  
pp. 1350064 ◽  
Author(s):  
CATARINA BASTOS ◽  
ORFEU BERTOLAMI ◽  
NUNO COSTA DIAS ◽  
JOÃO NUNO PRATA
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Dirac Equation ◽  
Energy Levels ◽  
Dirac Fermions ◽  
Two Dimensional ◽  
Dirac System ◽  
Noncommutative Parameter

We consider a noncommutative description of graphene. This description consists of a Dirac equation for massless Dirac fermions plus noncommutative corrections, which are treated in the presence of an external magnetic field. We argue that, being a two-dimensional Dirac system, graphene is particularly interesting to test noncommutativity. We find that momentum noncommutativity affects the energy levels of graphene and we obtain a bound for the momentum noncommutative parameter.

Dynamic Stability Analysis by Matrix Function

1987 ◽  
Vol 113 (7) ◽  
pp. 1085-1100 ◽  
Author(s):  
Tsunemi Shigematsu ◽  
Takashi Hara ◽  
Mitao Ohga
Keyword(s):  
Stability Analysis ◽  
Dynamic Stability ◽  
Matrix Function
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