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Perfectness of partial Christoffel transforms of Nikishin systems
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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BibTeX
@misc{kozhan2026perfectness,
title = {{Perfectness of partial Christoffel transforms of Nikishin systems}},
author = {Rostyslav Kozhan},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01395},
eprint = {2611.01395},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01395},
}
RIS
TY - UNPB
TI - Perfectness of partial Christoffel transforms of Nikishin systems
AU - Rostyslav Kozhan
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01395
UR - https://arxiv.org/abs/2611.01395
AB - 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=x_0. We show that if x_0 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.
ER -