Geodesic
Wave model of the Sturm--Liouville operator on an interval
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 48, Tome 471 (2018), pp. 225-260

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In the paper we construct the wave functional model of a symmetric restriction of the regular Sturm–Liouville operator on an interval. The model is based upon the notion of the wave spectrum and is constructed according to an abstract scheme which was proposed earlier. The result of the construction is a differential operator of the second order on an interval, which differs from the original operator only by a simple transformation. 
@article{ZNSL_2018_471_a13,
     author = {S. A. Simonov},
     title = {Wave model of the {Sturm--Liouville} operator on an interval},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {225--260},
     publisher = {mathdoc},
     volume = {471},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_471_a13/}
}
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S. A. Simonov. Wave model of the Sturm--Liouville operator on an interval. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 48, Tome 471 (2018), pp. 225-260. http://geodesic.mathdoc.fr/item/ZNSL_2018_471_a13/