On a certain difference equation and its application to the moment problem. (Q1889483)

The author considers the difference equation \[ | \sum_{m_1,m_2}\Omega[\sigma_{m_1,m_2}(z)]| =g(z),\quad z\in D \] where \(D\) is the unit square, \(g(z)\in A(D),\) \[ \sigma_{m_1,m_2}(z)=z+m_1 i+m_2,\quad | m_1| +| m_2| =2, \] and \(\Omega(z)\in A(cD)\) is an unknown function. Solution is sought in the class of even functions expressible as integrals of Cauchy type.