scholarly journals Spectral analysis for discontinuous non-self-adjoint singular Dirac operators with eigenparameter dependent boundary condition

2017 ◽  
Vol 453 (1) ◽  
pp. 304-316 ◽  
Author(s):  
Kun Li ◽  
Jiong Sun ◽  
Xiaoling Hao ◽  
Qinglan Bao
Keyword(s):  
Boundary Condition ◽  
Spectral Analysis ◽  
Dirac Operators

scholarly journals Spectral analysis of discrete dirac equation with generalized eigenparameter in boundary condition

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 6039-6054 ◽  
Author(s):  
Turhan Koprubasi ◽  
Ram Mohapatra
Keyword(s):  
Boundary Condition ◽  
Spectral Analysis ◽  
Dirac Equation ◽  
Dirac Operator ◽  
Spectral Properties ◽  
Difference Operators ◽  
Spectral Singularities ◽  
First Order ◽  
Complex Sequences

Let L denote the discrete Dirac operator generated in ?2 (N,C2) by the non-selfadjoint difference operators of first order (an+1y(2)n+1 + bny(2)n + pny(1)n = ?y(1)n, an-1y(1)n-1 + bny(1)n + qny(2)n = ?y(2)n, n ? N, (0.1) with boundary condition Xp k=0 (y(2)1?k + y(1)0 ?k)?k=0, (0.2) where (an), (bn), (pn) and (qn), n ? N are complex sequences, ?i; ?i ? C, i = 0, 1, 2,..., p and ? is a eigenparameter. We discuss the spectral properties of L and we investigate the properties of the spectrum and the principal vectors corresponding to the spectral singularities of L, if ?? n=1 |n|(|1-an| + |1+bn| + |pn| + |qn|) < ? holds.

scholarly journals Inverse spectral problem for Dirac operators by spectral data

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 1065-1077
Author(s):  
Ozge Akcay ◽  
Khanlar Mamedov
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Spectral Problem ◽  
Spectral Data ◽  
Spectral Parameter ◽  
Inverse Spectral Problem ◽  
Sufficient Conditions ◽  
Dirac Operators ◽  
Piecewise Continuous ◽  
Necessary And Sufficient

This work deals with the solution of the inverse problem by spectral data for Dirac operators with piecewise continuous coefficient and spectral parameter contained in boundary condition. The main theorem on necessary and sufficient conditions for the solvability of inverse problem is proved. The algorithm of the reconstruction of potential according to spectral data is given.

Separated Dirac operators and asymptotically constant linear systems

1997 ◽  
Vol 121 (1) ◽  
pp. 141-146 ◽  
Author(s):  
V. ARNOLD ◽  
H. KALF ◽  
A. SCHNEIDER
Keyword(s):  
Spectral Analysis ◽  
Linear Systems ◽  
Differential Operators ◽  
Dirac Operators ◽  
Levinson’S Theorem ◽  
Ordinary Differential Operators ◽  
Levinson Theorem

Levinson's theorem with all its ramifications is a well-established tool in the spectral analysis of ordinary differential operators (see in particular §§3·10, 11 and 4·3, 4 of Eastham's book [5]). In this note we should like to draw attention to a result that describes the solutions of asymptotically constant linear systems under weaker assumptions less precisely than the Levinson theorem. This result can be called the Perron–Lettenmeyer–Hartman–Wintner theorem after the contributions of these authors in [11, 10, 6, 8]. (Note that the Hartman–Wintner theorem that is discussed in [5, p. 17] is a substantially different version of this theorem.)

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