On the minimal property of de la Vallée Poussin's operator

Authors

  • B. Deregowska Faculty of Mathematics and Computer Science, Jagiellonian University
  • B. Lewandowska Faculty of Mathematics and Computer Science, Jagiellonian University

Keywords:

de la Vallee Poussin's operator, generalized projections, Dirichlet's kernel

Abstract

Let \( X = \mathcal{C}_0(2\pi)\) or \(X = L_1[0,2\pi]\). Denote by \(\Pi_n\) 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 Vallee Poussin's operator in the set of generalised projections \( \mathcal{P}_{\Pi_n}(X, \Pi_{2n-1})=\{P\in \mathcal{L}(X,\Pi_{2n-1}): P|_{\Pi_n}\equiv id \}.\) DOI: 10.1017/S0004972714000744

Published

2014-11-13

Issue

Vol. 91 No. 1 (2015)

Section

Articles
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