Markov function system

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A system () of linearly independent real-valued continuous functions defined on a finite interval and satisfying the condition: For any finite the functions form a Chebyshev system on .

Examples of Markov function systems are:

a) on any interval ;

b) on ;

c) on .


[1] N.I. [N.I. Akhiezer] Achiezer, "Theory of approximation" , F. Ungar (1956) (Translated from Russian)



[a1] E.W. Cheney, "Introduction to approximation theory" , Chelsea, reprint (1982)
[a2] W.J. Studden, "Tchebycheff systems: with applications in analysis and statistics" , Wiley (1966)
[a3] H.S. Shapiro, "Topics in approximation theory" , Springer (1971)
[a4] I.M. Singer, "Best approximation in normed linear spaces by elements of linear subspaces" , Springer (1970)
How to Cite This Entry:
Markov function system. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by N.P. KorneichukV.P. Motornyi (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article