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ON THE MINIMAL PROPERTY OF DE LA VALLÉE POUSSIN’S OPERATOR
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 91 / Issue 1 / February 2015
- Published online by Cambridge University Press:
- 08 October 2014, pp. 129-133
- Print publication:
- February 2015
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- Article
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Let
$X={\mathcal{C}}_{0}(2{\it\pi})$ or 
$X=L_{1}[0,2{\it\pi}]$. Denote by 
${\rm\Pi}_{n}$ the space of all trigonometric polynomials of degree less than or equal to 
$n$. The aim of this paper is to prove the minimality of the norm of de la Vallée Poussin’s operator in the set of generalised projections 
${\mathcal{P}}_{{\rm\Pi}_{n}}(X,\,{\rm\Pi}_{2n-1})=\{P\in {\mathcal{L}}(X,{\rm\Pi}_{2n-1}):P|_{{\rm\Pi}_{n}}\equiv \text{id}\}$.
