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Peer-reviewedCC BYAdvances in Computational Mathematics

G-invariant representations using coorbits: bi-Lipschitz properties

  • Radu Victor Balan1
  • Efstratios Tsoukanis2
  1. 1Department of Mathematics, University of Maryland, College Park, MD, USA
  2. 2Institute of Mathematical Sciences, Claremont Graduate University, Claremont, CA, USA
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Abstract

Let 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 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.

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Cite

BibTeXRIS
BibTeX
@article{balan2026ginvariant,
  title = {{G-invariant representations using coorbits: bi-Lipschitz properties}},
  author = {Radu Victor Balan and Efstratios Tsoukanis},
  journal = {Advances in Computational Mathematics},
  year = {2026},
  month = sep,
  doi = {10.1007/s10444-026-10363-y},
  url = {https://doi.org/10.1007/s10444-026-10363-y},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - G-invariant representations using coorbits: bi-Lipschitz properties
AU  - Radu Victor Balan
AU  - Efstratios Tsoukanis
PY  - 2026
DA  - 2026/09/24
JO  - Advances in Computational Mathematics
DO  - 10.1007/s10444-026-10363-y
UR  - https://doi.org/10.1007/s10444-026-10363-y
AB  - Let 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 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.
SN  - 1019-7168
SN  - 1572-9044
ER  -