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

Authors

  • Esra Kir Gazi University.
  • Gülen Bascanbaz-Tunca Ankara University.
  • Canan Yanik Hacettepe University.

DOI:

https://doi.org/10.4067/10.4067/S0716-09172005000100005

Keywords:

Spectrum, Spectral Singularities, Non-Selfadjoint System of Differential Equations.

Abstract

In this paper we investigated the spectrum of the operator L(?) generated in Hilbert Space of vector-valued functions L2 (R+, C2) by the system iy0 1 + q1 (x) y2 = ?y1, ?iy0 2 + q2 (x) y1 = ?y2 (0.1) , x ?R+ := [0,?), and the spectral parameter- dependent boundary condition (a1? + b1) y2 (0, ?) ? (a2? + b2) y1 (0, ?)=0, where ? 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 ?x |qi (x)|} < ?, i = 1, 2,?> 0, we proved that L(?) has a finite number of eigenvalues and spectral singularities with finite multiplicities. Furthermore we show that the principal functions corresponding to eigenvalues of L(?) belong to the space L2 (R+, {C2) and the principal functions corresponding to spectral singularities belong to a Hilbert space containing L2 (R+, C2).

Author Biographies

Esra Kir, Gazi University.

Faculty of Art and Science.

Gülen Bascanbaz-Tunca, Ankara University.

Department of mathematics, Faculty of Science.

Canan Yanik, Hacettepe University.

Department of Mathematics Education.

References

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Published

2017-04-20

How to Cite

[1]
E. Kir, G. Bascanbaz-Tunca, and C. Yanik, “Spectral properties of a non selfadjoint system of differential equations with a spectral parameter in the boundary condition”, Proyecciones (Antofagasta, On line), vol. 24, no. 1, pp. 49-63, Apr. 2017.

Issue

Vol. 24 No. 1 (2005)

Section

Artículos
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