Codimension-One Minimal Projections Onto Haar Subspaces
Haar subspace, Interpolating projection, Minimal projection
Journal of Approximation Theory
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.
Original Publication Date
DOI of published version
Lewicki, Grzegorz and Prophet, Michael, "Codimension-One Minimal Projections Onto Haar Subspaces" (2004). Faculty Publications. 3167.