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

An Huang; Yaojia Sun

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

Analysis of PDEs 2026-07-27 v1 Functional Analysis

Authors: An Huang , Yaojia Sun

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.

Keywords

vladimirov derivative bruhat-tits tree caffarelli-silvestre extension energy relations non-archimedean fractional laplacian

Cite

@article{arxiv.2607.24316,
  title  = {Energy relations for the generalised Vladimirov derivative via Bruhat-Tits tree extensions},
  author = {An Huang and Yaojia Sun},
  journal= {arXiv preprint arXiv:2607.24316},
  year   = {2026}
}