Approximation in AC(σ)

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...

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Bibliographic Details
Published in:Banach journal of mathematical analysis 2023, Vol.17 (1), Article 5
Main Authors: Doust, Ian, Leinert, Michael, Stoneham, Alan
Format: Article
Language:English
Subjects:
Functional Analysis
Mathematics
Mathematics and Statistics
Operator Theory
Original Paper
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Summary: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.
ISSN:2662-2033
1735-8787
DOI:10.1007/s43037-022-00229-y