On the Similarity of a $J$-Nonnegative Sturm–Liouville Operator to a Self-Adjoint Operator

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.