View source for Markov function system

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A system $\{\phi_\nu(x)\}_{\nu=1}^n$ ($n\leq\infty$) of linearly independent real-valued continuous functions defined on a finite interval $[a,b]$ and satisfying the condition: For any finite $k\leq n$ the functions $\phi_1(x),\ldots,\phi_k(x)$ form a [[Chebyshev system|Chebyshev system]] on $(a,b)$.

Examples of Markov function systems are:

a) $1,x,x^2,\ldots,$ on any interval $[a,b]$;

b) $1,\cos x,\cos2x,\ldots,$ on $[0,\pi]$;

c) $\sin x,\sin2x,\ldots,$ on $[0,\pi]$.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  N.I. [N.I. Akhiezer] Achiezer,   "Theory of approximation" , F. Ungar  (1956)  (Translated from Russian)</TD></TR></table>



====Comments====


====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  E.W. Cheney,   "Introduction to approximation theory" , Chelsea, reprint  (1982)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  W.J. Studden,   "Tchebycheff systems: with applications in analysis and statistics" , Wiley  (1966)</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  H.S. Shapiro,   "Topics in approximation theory" , Springer  (1971)</TD></TR><TR><TD valign="top">[a4]</TD> <TD valign="top">  I.M. Singer,   "Best approximation in normed linear spaces by elements of linear subspaces" , Springer  (1970)</TD></TR></table>