A spectral expansion for Schrödinger operator

• Bascanbaz-Tunca, Gülen ^[1]
  1. [1] Ankara University

     Ankara University

     Turquía

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 25, Nº. 1, 2006, págs. 63-78
• Idioma: inglés
• DOI: 10.4067/S0716-09172006000100005
• Enlaces
  • Texto completo
• Resumen

  • In this paper we consider the Schrödinger operator L generated inL²(R₊) byy''+q(x)y= µy, x∈R₊:= [0, ∞)subject to the boundary conditiony'(0)-hy(0)=0,where q is a complex valued function summable in [0, ∞ and h≠0 is a complex constant, µ is a complex parameter. We have assumed thatholds which is the minimal condition that the eigenvalues and the spectral singularities of the operator L are finite with finite multiplicities. Under this condition we have given the spectral expansion formula for the operator L using an integral representation for the Weyl function of L. Moreover we also have investigated the convergence of the spectral expansion.

• Referencias bibliográficas
  • Citas [1] E. Bairamov and A. O. Celebi, Spectrum and spectral expansion for the non-selfadjoint discrete Dirac operators, Quart. J. Math....
  • [2] E. Bairamov, Ö. Cakar and A. O. Celebi, Quadratic pencil of Schrödinger operators with spectral singularities: discrete spectrum and principal...
  • [3] Lyance, A differential Operator with Spectral Singularities, I,II, Amer. Math. Soc.Trans. Ser. 2, Vol. 60, 185-225, pp. 227-283, (1967).
  • [4] V. A. Marchenko, Expansion in eigenfunctions of Non-selfadjoint Singular Second-Order Differential Operators, A MS Translations, (2) 25,...
  • [5] V. A. Marchenko, Sturm-Liouville operators and applications Operator Theory: Advances and Applications, 22. Birkhäuser Verlag, Basel,...
  • [6] M.A.Naimark, Linear Differential Operators I-II, Ungar, New-York, (1968).
  • [7] J.T.Schwartz, Some non-selfadjoint operators, Comm. Pure and Appl.Math. 13, pp. 609-639, (1960).