The Schwarz problem for polyanalytic functions
A function \(f\) on an open subset \(G\) of the complex plane is called polyanalytic of order \(n\) if there are functions \(f_0,f_1,...,f_{n-1}\) analytic in \(G\) such that \[ f(z)=\bar z^{n-1}f_{n-1}(z)+\cdots+\bar zf_1(z)+f_0(z). \] The authors use the polyanalytic Schwarz kernel to give higher order Cauchy--Schwarz--Pompeiu representations and solve the Schwarz problem for the Poisson equation, Bitsadze equation, and the inhomigeneous polyanalytic equation.
scientific article; zbMATH DE number 5011359