Existence and properties of solutions of singular integro-differential equations on the real line (Q1873522)

The present paper deals with the justification of solvability conditions and properties of solutions for singular integro-differential equations (SIDE) with Cauchy kernel on the real line \(\mathbb{R}\). The investigation of SIDE on the real line is based on the construction of integral representations for analytic functions and their derivatives in the upper half-plane \(D^+ =\{ z\in \mathbb{C}: \operatorname {Im} z> 0\}\) or the lower half-plane \(D^- =\{z\in \mathbb{C}: \operatorname {Im} z< 0 \}\) of the complex plane \(\mathbb{C}\).