Geodesic
On the Similarity of a $J$-Nonnegative Sturm--Liouville Operator to a Self-Adjoint Operator
Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 1, pp. 81-84

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In terms of Weyl–Titchmarsh $m$-functions, we obtain a new necessary condition for an indefinite Sturm–Liouville operator to be similar to a self-adjoint operator. This condition is used to construct examples of $J$-nonnegative Sturm–Liouville operators with singular critical point zero.
Keywords: $J$-nonnegative operator, critical point, similarity to a self-adjoint operator. 
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     author = {I. M. Karabash and A. S. Kostenko},
     title = {On the {Similarity} of a $J${-Nonnegative} {Sturm--Liouville} {Operator} to a {Self-Adjoint} {Operator}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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I. M. Karabash; A. S. Kostenko. On the Similarity of a $J$-Nonnegative Sturm--Liouville Operator to a Self-Adjoint Operator. Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 1, pp. 81-84. http://geodesic.mathdoc.fr/item/FAA_2009_43_1_a5/