$$AC(\sigma)$$ spaces for polygonally inscribed curves

Al-shakarchi, Shaymaa; Doust, Ian

doi:10.1007/s43037-020-00110-w

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2022

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Cited by 2 publications

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“…By Property (5), the functions (x, y) ↦ g s (x) and (x, y) ↦ g s (y) are both in AC(Q ) with BV(Q ) norm equal to three. It follows that their product is also in AC 2 , and suppose that w ∈ B. As Q contained only one vertex point, namely the origin, then w is either a planar point or an edge point for f. As shown earlier, there is a compact neighbourhood V w of w such that f |V w ∈ AC(V w ).…”

Section: Without Loss Assume That a ′mentioning

confidence: 87%

Approximation in $$AC(\sigma )$$

Doust

Leinert

Stoneham

2022

Banach J. Math. Anal.

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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.

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Section: Without Loss Assume That a ′mentioning

confidence: 87%