Christoffel functions of measures on the real line with divergent logarithmic integral

Pavel Gubkin

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arXiv · 2608.14834

Christoffel functions of measures on the real line with divergent logarithmic integral

Pavel Gubkin

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Abstract

Let $\sigma$ be a Poisson-finite measure on the real line. If its logarithmic integral diverges, then the functions from the classical Hardy space $H^2$ with compactly supported Fourier transform are dense in $L^2(\mathbb{R}, \sigma)$. We give a quantitative version of this result, adapting the ideas from the 2020 paper by Borichev, Kononova and Sodin, where a similar question was studied in the setting of polynomial approximation.

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Pavel Gubkin. 2026-08-14. Christoffel functions of measures on the real line with divergent logarithmic integral. https://arxiv.org/abs/2608.14834

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