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arXiv · 2607.24316

Energy relations for the generalised Vladimirov derivative via Bruhat-Tits tree extensions

An Huang·Yaojia Sun
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Abstract

We formulate a proof on non-Archimedean analogue of the Caffarelli-Silvestre extension for fractional Laplacian on the Bruhat-Tits tree $T_p$ in terms of energy relations after identifying $\partial T_p$ with $\mathbb{P}^1(\mathbb{Q}_p)$, which reproduces the generalised Vladimirov derivative of the rescaled boundary function.

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An Huang, Yaojia Sun. 2026-07-27. Energy relations for the generalised Vladimirov derivative via Bruhat-Tits tree extensions. https://arxiv.org/abs/2607.24316

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