Abstract
If a continuous function f is approximated by elements of a Haar space in the maximum norm on an interval, the error curve of the best approximation has well known alternation properties. It is shown that if f is adjoined to the Haar space all zeros of the error function are monotonously increasing functions of the endpoints, and that under an additional hypothesis, the entire graph of the error curve is shifted to the left or right when the endpoints are moved accordingly.
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Zielke, R. Concertina-like movements of the error curve in the alternation theorem. Manuscripta Math 22, 229–234 (1977). https://doi.org/10.1007/BF01172665
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DOI: https://doi.org/10.1007/BF01172665