Approximation problems for polyanalytic functions

The talk will be devoted to problems of approximability of functions by polyanalytic rational functions and polynomials (i.e. by functions of the form $\overline{z}^nf_n(z)+...+\overline{z}f_1(z)+f_0$, where $f_0,f_1,...,f_n$ are rational functions/polynomials in the complex variables and $n$ is a positive integer) in norms of spaces of continuous and smooth functions on compact subsets of the complex plane. These subjects arisen at the end of 1970-th in the context of approximation problems for rational modules, and since the middle of 1990-th they are intensively studied in connection with problems on approximability of functions by solutions of general elliptic equations. It is planned to discuss the history of this topic and some recently obtained results.
The talk will be held in Russian.