NECESSARY AND SUFFICIENT CONDITIONS FOR THE SOLVABILITY OF INVERSE PROBLEM FOR A CLASS OF DIRAC OPERATORS

被引：4
作者：
Mamedov, Kh. R. [1 ,2 ]
Akcay, O. [1 ]
机构：
[1] Mersin Univ, Dept Math, TR-33343 Mersin, Turkey
[2] NAS Azerbaijan, Inst Math & Mech, AZ-1141 Baku, Azerbaijan
来源：
MISKOLC MATHEMATICAL NOTES | 2015年 / 16卷 / 01期
关键词：
Dirac operator; eigenvalues and normalizing numbers; inverse problem; necessary and sufficient conditions; SPECTRAL PARAMETER; BOUNDARY-CONDITION; SCATTERING PROBLEM; FINITE INTERVAL; SYSTEMS;
D O I：
10.18514/MMN.2015.1223
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we consider a problem for the first order Dirac differential equations system with spectral parameter dependent on boundary condition. The asymptotic behaviors of eigenvalues, eigenfunctions and normalizing numbers of this system are investigated. The expansion formula with respect to eigenfunctions is obtained and Parseval equality is given. The main theorem on necessary and sufficient conditions for the solvability of inverse problem is proved and the algorithm of reconstruction of potential from spectral data (the sets of eigenvalues and normalizing numbers) is given.
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收藏
页码：257 / 275
页数：19
相关论文
共 25 条
  • [1] NONLINEAR-EVOLUTION EQUATIONS OF PHYSICAL SIGNIFICANCE
    ABLOWITZ, MJ
    KAUP, DJ
    NEWELL, AC
    SEGUR, H
    [J]. PHYSICAL REVIEW LETTERS, 1973, 31 (02) : 125 - 127
  • [2] Albeverio S, 2005, RUSS J MATH PHYS, V12, P406
  • [3] Direct and inverse problems for the Dirac operator with a spectral parameter linearly contained in a boundary condition
    Amirov, R. Kh.
    Keskin, B.
    Ozkan, A. S.
    [J]. UKRAINIAN MATHEMATICAL JOURNAL, 2009, 61 (09) : 1365 - 1379
  • [4] On an inverse scattering problem for a class of Dirac operators with spectral parameter in the boundary condition
    Col, Aynur
    Mamedov, Kh. R.
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 393 (02) : 470 - 478
  • [5] de Monvel AB, 2004, ANN I FOURIER, V54, P1477
  • [6] Dzabiev T.T., 1966, DOKL AKAD NAUK AZER, V22, P8
  • [7] Freiling G., 2008, INVERSE STURM LIOUVI
  • [8] Skew-Self-Adjoint Dirac System with a Rectangular Matrix Potential: Weyl Theory, Direct and Inverse Problems
    Fritzsche, B.
    Kirstein, B.
    Roitberg, I. Ya.
    Sakhnovich, A. L.
    [J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 2012, 74 (02) : 163 - 187
  • [9] Gasymov M. G., 1966, AKAD NAUK AZERBAIDZA, V22, P3
  • [10] Gasymov M G., 1968, Trudy Moskov. Mat. Obsc, V19, P41
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