Speaker
Description
We plan to discuss the problems on uniform approximation of functions on compact sets in the complex plane by elements of polynomial modules of polyanalytic type generated by antiholomorphic functions and by polynomial solutions to general second-order elliptic but not strongly elliptic systems
of PDEs with constant coefficients. We will present some known and recent results in this topis and explore the special analytic characteristics of planar simply connected domains in terms of which the obtained approximation criteria are stated (the concept of a $g$-Nevanlinna domain, where $g$ is the
generator of the module by elements of which the approximation is carried out, and, the concept of an $L$-special domain, where $L$ is the elliptic differential operator that determines the corresponding system).
The talk is based on the results obtained in frameworks of the project 22--11--00071 by the Russian Science Foundation.
