Markov function system
From Encyclopedia of Mathematics
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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 
.
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
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