Spectral Analysis of Indefinite Sturm–Liouville Operators

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.