Abstract
Let \(D\) be a hexagon with two straight and four right angles. We consider a seven-element difference equation with holomorphic coefficients generated by this hexagon. A method for regularizing this equation is proposed. The solution is sought in the class of functions holomorphic outside the “half” of the boundary \(\partial D\) and vanishing at infinity. It is represented as a Cauchy-type integral over the half of the boundary with an unknown density. Applications to the problem of moments for entire functions of exponential type (EFET) are indicated.
