Absolutely Continuous Representing Measures of Moment Sequences with an Emphasis on the Regularity of the Densities

2024/11/05 by di Dio, Philipp J.
#26C05 #30E05 #44A60 #Algebraic Geometry (math.AG) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2411.03145

Abstract

In this work we investigate and characterize linear functionals L:ℝ[x₁,…,x_n]→ℝ with absolutely continuous representing measures μ, i.e., dμ(x) = g(x) d x for some density g. We focus on the regularity of g and how it is influenced/determined by the moments s_α= L(x^α).

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