Geodesic
Spectral Analysis of Indefinite Sturm--Liouville Operators
Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 3, pp. 88-92

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For a class of indefinite $J$-nonnegative Sturm–Liouville operators, we present a criterion of similarity to a self-adjoint operator. This criterion is formulated in terms of Weyl–Titchmarsh $m$-functions. Moreover, using this result, we obtain a criterion, as well as simple sufficient conditions, formulated in terms of the coefficients of a given Sturm–Liouville operator.
Keywords: Sturm–Liouville operator, $J$-nonnegative operator, critical point, similarity to a self-adjoint operator. 
@article{FAA_2014_48_3_a7,
     author = {A. S. Kostenko},
     title = {Spectral {Analysis} of {Indefinite} {Sturm--Liouville} {Operators}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {88--92},
     publisher = {mathdoc},
     volume = {48},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2014_48_3_a7/}
}
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A. S. Kostenko. Spectral Analysis of Indefinite Sturm--Liouville Operators. Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 3, pp. 88-92. http://geodesic.mathdoc.fr/item/FAA_2014_48_3_a7/