Work

G-invariant representations using coorbits: bi-Lipschitz properties

Year: 2026

Type: article

Abstract: Let $${\mathcal {V}}$$ V be a finite-dimensional real vector space with a finite group G acting orthogonally on it. We address the general problem of constructing Euclidean-stable embeddings of the orbit space $${\mathcal {V}}/G$$ V / G . Our approach builds on embeddings derived from subsets of sorted coorbits. The main result establishes that whenever such embeddings are injective, they are automatically bi-Lipschitz. Furthermore, we show that stable embeddings can be achieved in reduced dimensions, and that any continuous or Lipschitz G -invariant map can be factored through these embeddings.

Source: Advances in Computational Mathematics

DOI: 10.1007/s10444-026-10363-y

Authors: Radu Balan, Efstratios Tsoukanis

Institutions: University of Maryland, College Park, Claremont Graduate University

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: National Science Foundation