Square-induced interpolation problems for entire functions

Linear equations for functions that are analytic in the plane with cuts along the “half” of the square boundary have been considered. A method for their equivalent regularization has been proposed. The solution has been sought in the form of an integral of the Cauchy type with unknown density; the theory of the Carleman boundary value problem and the method of locally conformal pasting have been used. Applying the method of contracting mappings in a Banach space, the unconditional solvability of the obtained Fredholm integral equations of the second kind has been established. Applications of the moment problem for entire functions of the exponential type have been given. These problems are a generalization of the classical power-law problem of Stieltjes moments to the case of several rays with piecewise exponential weight.