Constructing measures with identical moments

Autor:	Kuznetsov, Alexey
Rok vydání:	2016
Předmět:	Mathematics - Classical Analysis and ODEs Mathematics - Complex Variables 30E05 30E20
Druh dokumentu:	Working Paper
Popis:	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. Comment: 10 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1607.08003 Zobrazit plný text záznamu View this record from Arxiv