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manuscripta mathematica

, Volume 22, Issue 3, pp 229–234 | Cite as

Concertina-like movements of the error curve in the alternation theorem

  • Roland Zielke
Article

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.

Keywords

Continuous Function Number Theory Error Function Algebraic Geometry Topological Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Cheney, E.W.: Introduction to Approximation Theory, McGraw-Hill, New York 1966.Google Scholar
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    Karlin, S. and Studden, W.J.: Tchebychev Systems: With Applications in Analysis and Statistics, John Wiley and Sons, New York 1966.Google Scholar
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    Streit, R.: Extremals and Zeros in Markov Systems are Monotone functions of one endpoint, J.Approximation Theory, to appear.Google Scholar
  4. [4]
    Zielke, R.: On Transforming on Tchebyshev-System into a Markov-System. J.Approximation Theory, 9 (1973), 357–366.Google Scholar
  5. [5]
    Zielke, R-: Alternation Properties of Tchebyshev-Systems and the Existence of adjoined functions, J.Approximation Theory, 10 (1974), 172–184.Google Scholar
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    Zielke, R.: Tchebyshev-Systems that cannot be Transformed into Markov-Systems, Manuscripta Mathematica, 17 (1975), 67–71.Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Roland Zielke
    • 1
  1. 1.Universität OsnabrückFachbereich 5BRD

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