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Completeness Theorem for Discontinuous Dirac Systems
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  • 作者:Hüseyin Tuna ; Aytekin Eryilmaz
  • 关键词:Dissipative Dirac operator ; Completeness of the system of eigenvectors and associated vectors ; Krein’s theorem ; 34L10 ; 34L40
  • 刊名:Differential Equations and Dynamical Systems
  • 出版年:2015
  • 出版时间:January 2015
  • 年:2015
  • 卷:23
  • 期:1
  • 页码:15-23
  • 全文大小:147 KB
  • 参考文献:1. Allahverdiev, B.P., Bairamov, E., Ugurlu, E.: Eigenparameter dependent Sturm–Liouville problems in boundary conditions with transmission conditions. J. Math. Anal. Appl. 401(1), 388-96 (2013) CrossRef
    2. Amirov, R.Kh: On a representation of solution of Dirac differential equation systems which have discontinuity in interval. Int. J. Pure Appl. Math. 12(3), 297-08 (2004)
    3. Bairamov, E., Ugurlu, E.: The determinants of dissipative Sturm–Liouville operators with transmission conditions. Math. Comput. Model 53, 805-13 (2011) CrossRef
    4. Bairamov, E., Ugurlu, E.: On the characteristic values of the real component of a dissipative boundary value transmission problem. Appl. Math. Comput. 218(19), 9657-663 (2012) CrossRef
    5. Bairamov E., Ugurlu E.: Krein’s theorems for a dissipative boundary value transmission problem. Complex. Anal. Oper. Theory. (2011). doi:10.1007/s11785-011-1180-z .
    6. Everitt, W.N., Hinton, D.B., Shaw, J.K.: The asymtotic form of the Titchmarsh–Weyl coefficient for Dirac systems. J. Lond. Math. Soc. 2(27), 465-67 (1983)
    7. Gohberg, I.C., Krein, M.G.: Introduction to the Theory of Linear Nonselfadjoint Operators. American Mathematical Society, Providence (1969)
    8. Guseinov, G.: Completeness theorem for the dissipative Sturm–Liouville operator. Turkish J. Math 17, 48-4 (1993)
    9. Guseinov, GSh, Tuncay, H.: The determinants of perturbation connected with a dissipative Sturm–Liouville operator. J. Math. Anal. Appl. 194, 39-9 (1995) CrossRef
    10. Kadakal, M., Mukhtarov, OSh: Discontinuous Sturm–Liouville problems containing eigenparameter in the boundary condition. Acta Math. Sinic Engl. Ser. Sep. 22(5), 1519-528 (2006) CrossRef
    11. Krein, M.G.: On the indeterminate case of the Sturm–Liouville boundary problem in the interval. Izv. Akad. Nauk SSSR Ser. Mat. 16(4), 293-24 (1952)
    12. Levitan, B.M., Sargsjan, I.S.: Sturm–Liouville and Dirac Operators. Mathematics and its Applications (Soviet Series). Kluwer Academic Publishers Group, Dordrecht (1991)
    13. Naimark M.A.: Linear Differential Operators, 2nd edn. Nauka, Moscow (1969) (English transl. of 1st edn, Part 1, 2, Frederick Ungar Publishing Co., New York (1968))
    14. Roos, B.W., Sangren, W.C.: Spectra for a pair of singular first order differential equations. Proc. Am. Math. 12, 468-76 (1961) CrossRef
    15. Roos B.W. Sangren W.C.: Spectra for a pair of first order differential equations, San Diego, CA. General Atomic Report GA 1373 (1960)
    16. Roos, B.W., Sangren, W.C.: Expansions associated with a pair of singular first-order differential equations. J. Math. Phys. 4, 999-008 (1963) CrossRef
    17. Shahriari, M., Jodayree Akbarfam, A., Teschl, G.: Uniqueness for inverse Sturm–Liouville problems with a finite number of transmission conditions. J. Math. Anal. 395(1), 19-9 (2012) CrossRef
    18. Titchmarsh, E.C.: Some eigenfunction expansion formulae. Proc. Lond. Math. Soc. 11, 159-68 (1961) CrossRef
    19. Titchmarsh, E.C.: A problem in relativistic quantum mechanics. Proc. Lond. Math. Soc. 3(11), 169-92 (1961) CrossRef
    20. Titchmarsh, E.C.: On the nature of the spectrum in problems of relativistic quantum mechanics
  • 刊物类别:Mathematics and Statistics
  • 刊物主题:Mathematics
  • 出版者:Springer India
  • ISSN:0974-6870
文摘
In this paper, we investigate the completeness of the system of rootvectors for discontinuous Dirac systems in the Weyl’s limit circle case, using Krein’s theorem.

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