G-invariant representations using coorbits: bi-Lipschitz properties
Abstract
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.
Fields of Study & Subjects
Advanced Operator Algebra Research
Geometric and Algebraic Topology
Advanced Algebra and Geometry
Publication details
- Journal / source
- Advances in Computational Mathematics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 52
- Issue
- 5
- Publication date
- 24 September 2026
- Language
- EN
- Document type
- Book chapter