%0 Journal Article
%T Spectral properties of singular Sturm-Liouville operators with indefinite weight sgn x
%A I. Karabash
%A C. Trunk
%J Mathematics
%D 2007
%I arXiv
%R 10.1017/S0308210507000686
%X We consider a singular Sturm-Liouville expression with the indefinite weight sgn x. To this expression there is naturally a self-adjoint operator in some Krein space associated. We characterize the local definitizability of this operator in a neighbourhood of $\infty$. Moreover, in this situation, the point $\infty$ is a regular critical point. We construct an operator $A=(\sgn x)(-d^2/dx^2+q)$ with non-real spectrum accumulating to a real point. The obtained results are applied to several classes of Sturm-Liouville operators.
%U http://arxiv.org/abs/0707.0865v1