Geodesic
Invariant transformations for the Sturm--Liouville operator
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 33, Tome 327 (2005), pp. 25-54

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In this paper we consider the Sturm–Liouville operator on a finite interval. For particular boundary conditions, a group of invariant transformations that preserve the operator's spectrum is constructed. This result permits us to reconsider some old problems for the Sturm–Liouville operator. In particular, the influence of this group on the inverse problem is discussed. 
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     author = {A. Vagharshakyan},
     title = {Invariant transformations for the {Sturm--Liouville} operator},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     publisher = {mathdoc},
     volume = {327},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_327_a2/}
}
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A. Vagharshakyan. Invariant transformations for the Sturm--Liouville operator. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 33, Tome 327 (2005), pp. 25-54. http://geodesic.mathdoc.fr/item/ZNSL_2005_327_a2/