International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 27, Pages 1437-1445
Spectral properties of the Klein-Gordon -wave equation with spectral parameter-dependent boundary condition
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
defined by the Klein-Gordon -wave equation
subject to the spectral parameter-dependent boundary condition
in the space , where , are complex
constants, is a complex-valued function. Discussing the
spectrum, we prove that has a finite number of
eigenvalues and spectral singularities with finite multiplicities
if the conditions , ,
, hold. Finally we show the properties of the
principal functions corresponding to the spectral singularities.