One-dimensional singular integral equations with coefficients vanishing on countable sets

On the basis of the principle of normalization of linear operators a general method is constructed for investigating one-dimensional singular integral equations in the space $L_p(\Gamma,\rho)$ in the case when their coefficients are degenerate on countable sets. In particular, zero sets satisfying the Carleson $\delta$-condition are studied, along with the images of such sets under linear fractional transformations.
Bibliography: 38 titles.