On the two dimensional singular integral equations (Q1174808)

The author introduces the ``equivalent curve'' method in order to discuss general solutions for the two-dimensional singular integral equation \(w(z)-\pi^{-1}q(z)\iint_G \bar w(\xi)(\bar\xi-\bar z)^{-2}d\sigma_\xi=f(z)\) where \(G\) is a simply connected region in the complex plane. He studies the case when \(| q(z)|=1\). \textit{I. N. Vekua} [Generalized analytic functions. Moscow: FizMatLit (1959; Zbl 0092.29703)]\ solved the equation under the condition \(| q(z)|<1\) and \textit{A. Dzhuraev} [Dokl. Akad. Nauk SSSR 197, 1251--1254 (1971; Zbl 0228.45002)]\ and \textit{I. I. Komyak} [Differ. Uravn. 16, 908--916 (1980; Zbl 0431.45002)]\ in the cases \(| q(z)|>1\) and \(q(z)=e^{i\lambda}\) (\(\lambda\) a real constant), respectively.