Markov Function System

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 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 $[0,\pi]$.

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