Approximation in $$AC(\sigma )$$

Abstract

For a nonempty compact subset $$\sigma$$ σ in the plane, the space $$AC(\sigma )$$ 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, $$C^1$$ C 1 functions and Lipschitz functions. In this paper, we examine analogues of these results in this more general setting.