On the dependence of uniform polyanalytic polynomial approximations on the order of polyanalyticity

Abstract

In this paper, we construct, for each n ∈ ℕ, a compact set X ⊂ ℂ (depending on n ) such that the set of all polyanalytic polynomials of order n is not dense in C( X ), but the set of all polyanalytic polynomials of order 2 n is already dense in C( X ).