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arXiv · 1312.1806

Approximation in $AC(\sigma)$

Ian Doust·Michael Leinert·Alan Stoneham
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Abstract

For a nonempty compact subset $\sigma$ in the plane, the space $AC(\sigma)$ 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.

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Ian Doust, Michael Leinert, Alan Stoneham. 2013-12-06. Approximation in $AC(\sigma)$. https://doi.org/10.1007/s43037-022-00229-y

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