Constructing measures with identical moments

Kuznetsov, Alexey

doi:10.1090/proc/13585

Constructing measures with identical moments
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by Alexey Kuznetsov PDF

Proc. Amer. Math. Soc. 145 (2017), 4431-4441 Request permission

Abstract:

When the moment problem is indeterminate, 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.

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