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arXiv · 2602.00187

Harmonic projection and hypercentral extensions

Antoine Gournay
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Abstract

The Liouville property is a strong form of amenability, but contrary to amenability, it is not well-behaved under extensions. In this paper it is shown that, for some measures, the Liouville property is preserved by [FC-]hypercentral extensions. To this end a projection from $\ell^\infty$ onto the space of harmonic functions is introduced.

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Antoine Gournay. 2026-01-30. Harmonic projection and hypercentral extensions. https://arxiv.org/abs/2602.00187

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