Perfectness of partial Christoffel transforms of Nikishin systems
Rostyslav Kozhan
Abstract
We study multiple orthogonal polynomial systems obtained from a Nikishin system of two measures by applying a Christoffel transform to one of the measures at a point x=x0. We show that if x0 separates the supports of the generating measures, then the modified systems remain perfect. As an application, we prove that the type I multiple orthogonal polynomials of a Nikishin system have no zeros in the gap between the supports of its generating measures.
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