A singular integral equation with the Cauchy kernel on a closed interval in a class of distributions (Q2388013)

The author investigates an analogue of the singular integral equation \[ \frac{1}{2\pi} \int_{a}^{b} \frac{\varphi(x)\,dx}{x_{0}-x} = g(x_{0}), \quad x_{0}\in(a,b) \] for the case when the right-hand side and the unknown function are distributions of some class. For this purpose he uses a version of the classical approach reducing the solution to a boundary value problem for analytic functions. It should be noted that the author mentions no papers dealing with singular integral equations in the spaces of distributions [see, e.g. the book \textit{S. Prößdorf}, Einige Klassen singulärer Gleichungen, Akademie-Verlag, Berlin (1974; Zbl 0302.45008)].