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arXiv · 2603.23643

Approximation theorems in bilipschitz invariant theory

Jameson Cahill·Joseph W. Iverson·Dustin G. Mixon·Nathan Willey
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Abstract

Bilipschitz invariant theory concerns low-distortion embeddings of orbit spaces into Euclidean space. To date, embeddings with the smallest-possible distortion are known for only a few cases, to include: (a) planar rotations, (b) real phase retrieval, and (c) finite reflection groups. Here, we prove that for all three of these cases, the smallest possible distortion is nearly achieved by a composition of a "max filter bank" with a linear transformation. Our proof amounts to a two-step process: first, we show it suffices to demonstrate a certain inclusion of Lipschitz function spaces, and second, we prove that inclusion, using fundamentally different approaches for the three cases. We also show that these cases interact differently with a few related function spaces, which suggests that a unified treatment would be nontrivial.

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BibTeXRIS

Jameson Cahill, Joseph W. Iverson, Dustin G. Mixon, Nathan Willey. 2026-03-24. Approximation theorems in bilipschitz invariant theory. https://arxiv.org/abs/2603.23643

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