Spectral properties of a non selfadjoint system of differential equations with a spectral parameter in the boundary condition

• Kir, Esra ^[1] ; Bascanbaz-Tunca, Gülen ^[2] ; Yanik, Canan ^[3]
  1. [1] Gazi University

     Gazi University

     Turquía

     
  2. [2] Ankara University

     Ankara University

     Turquía

     
  3. [3] Hacettepe University

     Hacettepe University

     Turquía

     

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• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 24, Nº. 1, 2005, págs. 49-63
• Idioma: inglés
• DOI: 10.4067/10.4067/S0716-09172005000100005
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• Resumen

  • In this paper we investigated the spectrum of the operator L(λ) generated in Hilbert Space of vector-valued functions L2 (R+, C2) by the system iy0 1 + q1 (x) y2 = λy1, −iy0 2 + q2 (x) y1 = λy2 (0.1) , x ∈R+ := [0,∞), and the spectral parameter- dependent boundary condition (a1λ + b1) y2 (0, λ) − (a2λ + b2) y1 (0, λ)=0, where λ is a complex parameter, qi, i = 1, 2 are complex-valued functions ai 6= 0, bi 6= 0, i = 1, 2 are complex constants. Under the condition sup x∈R+ {exp εx |qi (x)|} < ∞, i = 1, 2,ε> 0, we proved that L(λ) has a finite number of eigenvalues and spectral singularities with finite multiplicities. Furthermore we show that the principal functions corresponding to eigenvalues of L(λ) belong to the space L2 (R+, {C2) and the principal functions corresponding to spectral singularities belong to a Hilbert space containing L2 (R+, C2).

• Referencias bibliográficas
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