Some properties of Markov systems (Q803455)

Let A be a subset of the real line with at least \(n+2\) elements and I(A) be the convex hull of A. A sequence of functions \(Z_ n=\{z_ 0,...,z_ n\}\) defined on A is called a (weak) Chebyshev system if it is linearly independent and for all points \(x_ 0....x_ n\) in A, \(\det \{z_ i(x_ j)\}^ n_{i,j=0}>0(\geq 0)\). If \(Z_ k\) is a (weak) Chebyshev system for \(k=0,...,n\), then the \(Z_ n\) is said to be a (weak) Markov system. In this paper the authors demonstrate some new properties of Markov systems, involving generalized divided differences, relative differentiation, and weak nondegeneracy.