Markov interlacing property for perfect splines
The author proves the following generalization of the classical V. A. Markov theorem concerning algebraic polynomials. If the zeros of two perfect splines of a fixed degree interlace, then the zeros of their derivatives also interlace. Recall that a perfect spline of degree \(r\) is an expression of the form \[ p(t):= \sum^r_{j=1} \alpha_j t^{j-1}+ c\Biggl[t^r+ 2 \sum^{n-r}_{i= 1}(-1)^i(t- \xi_i)^r_+\Biggr] \] with real \(\alpha_j\) and \(c_j\) as usual, \(t_+:= \max\{t,0\}\).
scientific article; zbMATH DE number 1356337