We consider an indefinite Sturm-Liouville operator in the polar form in a weighted space with a non-odd weight with one turning point at 0.
For an operator with a discrete spectrum, we find new criteria for the operator to have Riesz basis property. In the singular case, the problem of similarity to a selfadjoint operator is studied. The results are based on a joint work with Branko Curgus (WWU, Bellingham, Washington) and Carsten Trunk (TU Ilmenau, Germany).