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, Volume 7, Issue 4, pp 325–329 | Cite as

A remark on periodic Tchebyshev systems

  • Roland Zielke


The linear hull of a Tchebyshev system is called a Haarspace. Every Haar-space of periodic functions has odd dimension. It is shown that under certain conditions an n-dimensional Haar-space of periodic functions contains i-dimensional Haar-spaces Ui, i=1,3,...,n, with U1⊂U3⊂...⊂Un=U.


Number Theory Periodic Function Algebraic Geometry Topological Group Linear Hull 
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    CHENEY, E.W.: Introduction to Approximation Theory, Mc Graw-Hill, 1966.Google Scholar
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    KARLIN, S. and W.J. STUDDEN: Tchebycheff Systems: With Apllications in Analysis and Statistics. John Wiley and Sons, 1966.Google Scholar
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    NEMETH, A.B.: Transformations of the Chebyshev Systems. Mathematica (Cluj) 8, 315–333, 1966.Google Scholar
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    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, 307–310, 1969.Google Scholar
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    ZIELKE, R.: On Transforming a Tchebyshev-System into a Markov-System. Journal of Approximation Theory, to appear.Google Scholar

Copyright information

© Springer-Verlag 1972

Authors and Affiliations

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

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