DOIAbstract
AbstractLet Un be an extended Tchebycheff system on the real line. Given a point x¯=(x1,…,xn), where x1<⋯<xn, we denote by f(x¯;t) the polynomial from Un, which has zeros x1,…,xn. (It is uniquely determined up to multiplication by a constant.) The system Un has the Markov interlacing property (M) if the assumption that x¯ and y¯ interlace implies that the zeros of f′(x¯;t) and f′(y¯;t) interlace strictly, unless x¯=y¯. We formulate a general condition which ensures the validity of the property (M) for polynomials from Un. We also prove that the condition is satisfied for some known systems, including exponential polynomials ∑i=0nbieαix and ∑i=0nbie−(x−βi)2. As a corollary we obtain that property (M) holds true for Müntz polynomials ∑i=0nbix...
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