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arXiv · 0707.0865

Spectral properties of singular Sturm-Liouville operators with indefinite weight sgn x

I. Karabash·C. Trunk
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Abstract

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.

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I. Karabash, C. Trunk. 2007-07-05. Spectral properties of singular Sturm-Liouville operators with indefinite weight sgn x. https://doi.org/10.1017/s0308210507000686

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