Growth properties of Nevanlinna matrices for rational moment problems

[摘要] We consider rational moment problems on the real line with their associated orthogonal rational functions. There exists a Nevanlinna-type parameterization relating to the problem, with associated Nevanlinna matrices of functions having singularities in the closure of the set of poles of the rational functions belonging to the problem. We prove results related to the growth at the singularities of the functions in a Nevanlinna matrix, and in particular provide bounds on the growth analogous to the corresponding result in the classical polynomial case, when the number of singularities is finite. (C) 2010 Elsevier Inc. All rights reserved.

[发布日期] 2010-12-01

[关键词] Rational moment problems;Orthogonal rational functions;Nevanlinna parameterization;Riesz-type criterion;Growth estimates