Growth properties of Nevanlinna matrices for rational moment problems

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. Key words: rational moment problems, orthogonal rational functions, Nevanlinna parameterization, Riesz type criterion, growth estimates 2000 MSC: 30D15, 30E05, 42C05, 44A60

• Type: Journal
• Year: 2010
• Where: JAT
• Authors: Adhemar Bultheel, Pablo González-Vera, Erik Hendriksen, Olav Njåstad
• Keywords: JAT 2010, Orthogonal Rational Functions, Rational Functions, Rational Moment Problems