2016/07/27 by Alexey Kuznetsov, Kuznetsov, Alexey · 1 citation
Computer Science · Mathematics · #30E05 #30E20 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials #Matrix Theory and Algorithms #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1607.08003
openalex publication_date 2016/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Nevanlinna parametrization establishes a bijection between the class of all measures having a prescribed set of moments and the class of Pick functions. The fact that all measures constructed through the Nevanlinna parametrization have identical moments follows from the theory of orthogonal polynomials and continued fractions. In this paper we explore the opposite direction: we construct a set of measures and we show that they all have identical moments, and then we establish a Nevanlinna-type parametrization for this set of measures. Our construction does not require the theory of orthogonal polynomials and it exposes the analytic structure behind the Nevanlinna parametrization.