Inverse problem for dirac system with singularities in interior points

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• 作者：Oleg Gorbunov ; Viacheslav Yurko
• 关键词：Differential systems ; Singularity ; Spectral analysis ; Inverse problems ; 34A55 ; 34L40 ; 34A36 ; 47E05
• 刊名：Analysis and Mathematical Physics
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：6
• 期：1
• 页码：1-29
• 全文大小：602 KB
• 参考文献：1.Meschanov, V.P., Feldstein, A.L.: Automatic Design of Directional Couplers. Sviaz, Moscow (1980) (in Russian)
  2.Litvinenko, O.N., Soshnikov, V.I.: The Theory of Heterogenious Lines and their Applications in Radio Engineering. Radio, Moscow (1964) (in Russian)
  3.Freiling, G., Yurko, V.A.: Reconstructing parameters of a medium from incomplete spectral information. Results Math. 35, 228–249 (1999)
  4.Lapwood, F.R., Usami, T.: Free Oscillations of the Earth. Cambridge University Press, Cambridge (1981)MATH
  5.Wasow, W.: Linear Turning Point Theory. Applied Mathematical Sciences, vol. 54. Springer, New York (1985)
  6.Gasymov, M.G.: Determination of Sturm–Liouville equation with a singular point from two spectra. Dokl. Akad. Nauk. SSSR 161, 274–276 (1965) [Transl. in Sov. Math. Dokl. 6, 396–399 (1965)]
  7.Zhornitskaya, L.A., Serov, V.S.: Inverse eigenvalue problems for a singular Sturm–Liouville operator on (0,1). Inverse Probl. 10(4), 975–987 (1994)CrossRef MathSciNet MATH
  8.Yurko, V.A.: Inverse problem for differential equations with a singularity. Differ. Uravn. 28, 1355–1362 (1992) [English transl. in Differ. Equ. 28, 1100–1107 (1992)]
  9.Yurko, V.A.: On higher-order differential operators with a singular point. Inverse Probl. 9, 495–502 (1993)CrossRef MathSciNet MATH
  10.Yurko, V.A.: On higher-order differential operators with a regular singularity. Mat. Sb. 186(6), 133–160 (1995) [English transl. in Sb. Math. 186(6), 901–928 (1995)]
  11.Yurko, V.A.: Integral transforms connected with differential operators having singularities inside the interval. Integral Transforms Spec. Funct. 5(3–4), 309–322 (1997)CrossRef MathSciNet MATH
  12.Gorbunov, O.B., Yurko, V.A., Shieh, C.-T.: Spectral analysis of the Dirac system with a singularity in an interior point. arXiv:​1410.​2020v1 [math.SP]
  13.Yurko, V.A.: Method of Spectral Mappings in the Inverse Problem Theory. Inverse and Ill-Posed Problems Series. VSP, Utrecht (2002)CrossRef MATH
  14.Freiling, G., Yurko, V.A.: Inverse Sturm–Liouville Problems and their Applications. Nova Science Publishers, Inc., Huntington (2001)MATH
  15.Bellmann, R., Cooke, K.: Differential-Difference Equations. Academic Press, New York (1963)
  
• 作者单位：Oleg Gorbunov (1)
  Viacheslav Yurko (1)
  
  1. Department of Mathematics, Saratov State University, Astrakhanskaya 83, Saratov, 410012, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis
  Mathematical Methods in Physics
  
• 出版者：Birkh盲user Basel
• ISSN：1664-235X

文摘

We study the non-selfadjoint Dirac system on a finite interval having non-integrable regular singularities in interior points with additional matching conditions at these points. Properties of spectral characteristics are established, and the inverse spectral problem is investigated. We provide a constructive procedure for the solution of the inverse problem, and prove its uniqueness. Moreover, necessary and sufficient conditions for the global solvability of this nonlinear inverse problem are obtained. Keywords Differential systems Singularity Spectral analysis Inverse problems