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Integral representation of Markov systems and the existence of adjoined functions for Haar spaces. (English) Zbl 0724.41031

Author’s abstract: “Let A be a set of real numbers, and let \(Y_ n=\{y_ 0,...,y_ n\}\) be a Chebyshev system on A. Assume, moreover, that if int A or sup A belong to A, then it is a point of accumulation of A at which all \(y_ j\) are continuous. We find necessary and sufficient conditions for the existence of a function \(y_{n+1}\) such that \(\{y_ 0,...,y_ n,y_{n+1}\}\) is a Chebyshev system on A. This theorem generalizes earlier results of Zielke and of the author. The proof is based on an integral representation of Markov systems that slightly extends a previous result of Zielke.”
Reviewer: E.Deeba (Houston)

MSC:

41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A50 Best approximation, Chebyshev systems
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