On Riemann boundary value problem for polyanalytic functions on the real axis (Q812471)

What is called in the paper the Riemann boundary value problem for polyanalytic functions, involves the usual condition \(V^+(x)=G_0(x)V^-(x)+f_0(x)\) on the boundary for the looked-for function \(V\) and the similar conditions for its derivatives up to be order \(n-1\), with \(n\) being the order of polyanaliticity, and restrictions on the asymptotic behavior at infinity. The problem reduces to the matrix Riemann problem with the coefficient of a special form which allows the authors, to obtain an expression for the solution of the homogeneous problem, as well as a necessary and sufficient condition for solvability of the non-homogeneous one. The methods used are rather classic.