Journal of Approximation Theory vol:162 issue:12 pages:2184-2201
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.