Spectral expansion of Sturm-Liouville problems with eigenvalue-dependent boundary conditions

In this paper, we consider the operator L generated in L₂(R₊) by the differential expression

___

  • Naimark, M.A., Investigation of the spectrum and the expansion in eigenfunctions of a non-selfadjoint operator of the second order on a semi-axis, American Mathematical Society Translations Series 2, 16, (1960), 103--193.
  • Lyance, V.E., A differential operator with spectral singularities I, II, American Mathematical Society Transactions Series 2, 60, (1967), 185--225, 227--283.
  • Gasymov, M.G. and Maksudov, F.G., The principal part of the resolvent of non-selfadjoint opeerators in neighbourhood of spectral singularities, Func. Anal. Appl, 6, (1972), 185--192.
  • Maksudov, F.G. and Allakhverdiev, B.P., Spectral analysis of a new class of non-selfadjoint operators with continuous and point spectrum, Soviet Math. Dokl., 30, (1984), 566--569.
  • Adıvar, M. and Bairamov, E., Spectral properties of non-selfadjoint difference operators, Journal of Mathematical Analysis and Applications, 261(2), (2001), 461--478.
  • Bairamov, E., Çakar, Ö. and Yanık, C., Spectral singularities of the Klein-Gordon s-wave equation, Indian Journal of Pure and Applied Mathematics, 32(6), (2001), 851--857.
  • Bairamov, E. and Çelebi, A.O., Spectrum and spectral expansion for the non-selfadjoint discrete Dirac operators, The Quarterly Journal of Mathematics. Oxford Second Series, 50(200), (1999), 371--384.
  • Bairamov, E. and Karaman, Ö., Spectral singularities of the Klein-Gordon s-wave equations with and integral boundary conditions, Acta Mathematica Hungarica, 97(1--2), (2002), 121--131.
  • Krall, A.M., Bairamov, E. and Çakar, Ö., Spectrum and spectral singularities of a quadratic pencil of a Schrödinger operator with a general boundary condition, Journal of Differential Equations, 151(2), (1999), 252--267.
  • Krall, A.M., Bairamov, E. and Çakar, Ö., Spectral analysis of non-selfadjoint discrete Schrödinger operators with spectral singularities, Mathematische Nachrichten, 231, (2001), 89--104.
  • Marchenko, V.A., Expansion in eigenfunctions of non-selfadjoint singular second-order differential operators, American Mathematical Society Transactions Series 2, 25, (1963), 99.77--130.
  • Başcanbaz-Tunca, G, Spectral expasion of a non-selfadjoint differential operator on the whole axis, J.Math.Anal.Appl., 252(1), (2000), 278--297.
  • Kır Arpat, E., An eingenfunction expansion of the non-selfadjoint Sturm-Liouville operator with a singular potential, Journal of Mathematical Chemistry, 51(8), (2013), 2196--2213.
  • Bairamov, E. and Yokuş, N., Spectral singularities of Sturm-Liouville problems with eigenvalue-dependent boundary conditions, Abstract and Applied Analysis, 2009, Article ID 289596, (2009), 8 pages.
  • Yokuş, N., Principal functions of non-selfadjoint sturm-liouville problems with eigenvalue-dependent boundary conditions, Abstract and Applied Analysis, 2011, Article ID 358912, (2011), 12 pages.