Faculty Publications

Codimension-One Minimal Projections Onto Haar Subspaces

Document Type

Article

Keywords

Haar subspace, Interpolating projection, Minimal projection

Journal/Book/Conference Title

Journal of Approximation Theory

Volume

127

Issue

2

First Page

198

Last Page

206

Abstract

Let Hn be an n-dimensional Haar subspace of X = Cℝ[a, b] and let Hn-1 be a Haar subspace of Hn of dimension n - 1. In this note we show (Theorem 6) that if the norm of a minimal projection from Hn onto Hn-1 is greater than 1, then this projection is an interpolating projection. This is a surprising result in comparison with Cheney and Morris (J. Reine Angew. Math. 270 (1974) 61 (see also (Lecture Notes in Mathematics, Vol. 1449, Springer, Berlin, Heilderberg, New York, 1990, Corollary III.2.12, p. 104) which shows that there is no interpolating minimal projection from C[a, b] onto the space of polynomials of degree ≤n, (n≥2). Moreover, this minimal projection is unique (Theorem 9). In particular, Theorem 6 holds for polynomial spaces, generalizing a result of Prophet [(J. Approx. Theory 85 (1996) 27), Theorem 2.1]. © 2004 Elsevier Inc. All rights reserved.

Department

Department of Mathematics

Original Publication Date

1-1-2004

DOI of published version

10.1016/j.jat.2004.03.002

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