Approximation in \(AC(\sigma)\)

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...

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Bibliographic Details
Published inarXiv.org
Main Authors Doust, Ian, Leinert, Michael, Stoneham, Alan
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 02.06.2022
Subjects
Continuity (mathematics)
Mathematical analysis
Operators (mathematics)
Tornadoes
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1312.1806