Spectral properties of singular Sturm-Liouville operators with indefinite weight sgnx
نویسنده
چکیده
We consider a singular Sturm-Liouville expression with the indefinite weight sgnx. 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 ∞. Moreover, in this situation, the point ∞ is a regular critical point. We construct an operator A = (sgnx)(−d2/dx2 + 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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