International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 27, Pages 1437-1445

Spectral properties of the Klein-Gordon s-wave equation with spectral parameter-dependent boundary condition

Gülen Başcanbaz-Tunca

Department of Mathematics, Faculty of Science, Ankara University, Tandogan, Ankara 06100, Turkey

Received 12 March 2002

Copyright © 2004 Gülen Başcanbaz-Tunca. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We investigate the spectrum of the differential operator Lλ defined by the Klein-Gordon s-wave equation y+(λq(x))2y=0, x+=[0,), subject to the spectral parameter-dependent boundary condition y(0)(aλ+b)y(0)=0 in the space L2(+), where a±i, b are complex constants, q is a complex-valued function. Discussing the spectrum, we prove that Lλ has a finite number of eigenvalues and spectral singularities with finite multiplicities if the conditions limxq(x)=0, supxR+{exp(ϵx)|q(x)|}<, ϵ>0, hold. Finally we show the properties of the principal functions corresponding to the spectral singularities.