Schwartz's integral for a class of functions which are regular in a denumerable-connected circular $\delta$-region

We construct an expression which generalizes the familiar Schwartz expression to the case of a denumerable-connected circular $\delta$-region for which the centers of the boundary circles lie on a finite number of straight lines of the same bundle. Using this expression we can construct a regular and single-valued function of a sufficiently general form inside the region under consideration, from the values of its real part on the boundary of the region.