Geodesic
Embedded spectrum on a metric graph (an observation)
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 215-220 Cet article a éte moissonné depuis la source Math-Net.Ru

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An elementary example of a simplest star-like graph which shows that the analytical disjunction may occur not on only at isolated points of the spectral parameter, but also on whole intervals, are suggested. 
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V. L. Oleinik; B. S. Pavlov. Embedded spectrum on a metric graph (an observation). Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 215-220. http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a20/

[1] V. Bogevolnov, A. Mikhailova, B. Pavlov, A. Yafyasov, “About scattering on the ring”, Operator Theory: Advances and Application, 124, Birkhauser Verlag, Basel, 2001, 155–187 | MR