Abstract
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.
Similar content being viewed by others
References
CHENEY, E.W.: Introduction to Approximation Theory, Mc Graw-Hill, 1966.
KARLIN, S. and W.J. STUDDEN: Tchebycheff Systems: With Apllications in Analysis and Statistics. John Wiley and Sons, 1966.
NEMETH, A.B.: Transformations of the Chebyshev Systems. Mathematica (Cluj) 8, 315–333, 1966.
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.
ZIELKE, R.: On Transforming a Tchebyshev-System into a Markov-System. Journal of Approximation Theory, to appear.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zielke, R. A remark on periodic Tchebyshev systems. Manuscripta Math 7, 325–329 (1972). https://doi.org/10.1007/BF01644071
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01644071