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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Vydáno v:Banach journal of mathematical analysis Ročník 17; číslo 1
Hlavní autoři: Doust, Ian, Leinert, Michael, Stoneham, Alan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 01.01.2023
Témata:
Functional Analysis
Mathematics
Mathematics and Statistics
Operator Theory
Original Paper
26B30
Functions of bounded variation
47B40
Absolutely continuous functions
ISSN:2662-2033, 1735-8787
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Popis
Shrnutí: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