# Markov function system

From Encyclopedia of Mathematics

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 .

#### References

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

#### Comments

#### References

[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: http://encyclopediaofmath.org/index.php?title=Markov_function_system&oldid=12310

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