Approximation in AC(σ) - Doust, Ian; Leinert, Michael; Stoneham, Alan (Banach journal of mathematical analysis, 2023)
For a nonempty compact subset σ in the plane, the space A C ( σ ) is the closure of the space of complex polynomials in two real variables under a particular variation norm. In the classical setting, AC [0, 1] contains several other useful dense subsets, such as continuous piecewise linear functions, C 1 functions and Lipschitz functions. In this paper, we examine analogues of these results in this more general setting.