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Interpolation by Weak Chebyshev Spaces

✍ Scribed by Oleg Davydov; Manfred Sommer

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 214 KB
Volume: 102
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1999.3412

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✦ Synopsis

We present two characterizations of Lagrange interpolation sets for weak Chebyshev spaces. The first of them is valid for an arbitrary weak Chebyshev space U and is based on an analysis of the structure of zero sets of functions in U extending Stockenberg's theorem. The second one holds for all weak Chebyshev spaces that possess a locally linearly independent basis.

2000 Academic Press

1. Introduction

Let U denote a finite-dimensional subspace of real valued functions defined on a totally ordered set K, for example, an arbitrary subset of R.

A finite subset T=[t 1 , ..., t n ] of K, where n=dim U, is called an interpolation set (I-set) w.r.t. U if for any given data [ y 1 , ..., y n ] there exists a unique function u # U such that u(t i )= y i , i=1, ..., n.

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