Approximation by random complex polynomials and rational functions

TL;DR

This paper explores the use of random complex polynomials and rational functions to extend classical approximation theorems and examines properties of random compact sets related to complex approximation.

Contribution

It introduces random analogs of classical approximation theorems and studies their implications for random compact sets in complex analysis.

Findings

Development of random approximation theorems

Analysis of properties of random compact sets

Extension of classical results to probabilistic settings

Abstract

We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.