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, Volume 17, Issue 1, pp 67–71 | Cite as

Tchebyshev systems that cannot be transformed into Markov systems

  • Roland Zielke


The linear hull of a Tchebyshev system is called a Haar-space. A basis f1,...,fn of an n-dimensional Haar-space is called a Markov basis if f1,...,fi form a Tchebyshev system for each i=l,...,n. It is shown by suitable examples that for all n≥3 there exist Haar-spaces without a Markov basis.


Number Theory Algebraic Geometry Topological Group Linear Hull Markov System 
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  1. [1]
    Hadeler, K.P.: Remarks on Haar systems. J.Appr.Th. 7, 59–62, 1973.Google Scholar
  2. [2]
    Karlin, S. and W.J.Studden: Tchebyshev systems: With applications in analysis and statistics. John Wiley and Sons, 1966.Google Scholar
  3. [3]
    Nemeth, A.B.: Transformations of the Chebyshev Systems. Mathematica (Cluj) 8, 315–333, 1966.Google Scholar
  4. [4]
    Nemeth, A.B.: About the extension of the domain of definition of the Chebyshev systems defined on intervals of the real axis. Mathematica (Cluj) 11 (1969), 307–310.Google Scholar
  5. [5]
    Obreschkoff, N.: Verteilung und Berechnung der Nullstellen reeller Polynome. VEB Deutscher Verlag d. Wiss., Berlin, 1966.Google Scholar
  6. [6]
    Volkov, V.I.: Some properties of Chebyshev systems, Kalinin Gos. Ped. Inst. Uc. Zap. 26, 41–48, 1958.Google Scholar
  7. [7]
    Zielke, R.: On transforming a Tchebyshev-system into a Markov-system. J. of Appr. Th., 9 (1973), 357–366.Google Scholar
  8. [8]
    Zie1ke, P.: Alternation properties of Tchebyshev-systems and the existence of adjoined functions, 10 (1974), 172–184Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Roland Zielke
    • 1
  1. 1.Lehrstuhl für Biomathematik der Universität TübingenTübingenDeutschland

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