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Non-real eigenvalues of singular indefinite Sturm-Liouville operators
We study a Sturm-Liouville expression with indefinite weight of the form $\mathrm {sgn}(-d^2/dx^2+V)$ on $\mathbb {R}$ and the non-real eigenvalues of an associated selfadjoint operator in a Krein space. For real-valued potentials $V$ with a certain behaviour at $\pm \infty$ we prove that there are no real eigenvalues and that …