Stable Coorbit Embeddings of Orbifold Quotients
<|reference_start|>Stable Coorbit Embeddings of Orbifold Quotients: Given a real inner product space $V$ and a group $G$ of linear isometries, we construct a family of $G$-invariant real-valued functions on $V$ that we call coorbit filter banks, which unify previous notions of max filter banks and finite coorbit filter banks. When $V=\mathbb R^d$ and $G$ is compact, we establish that a suitable coorbit filter bank is injective and locally lower Lipschitz in the quotient metric at orbits of maximal dimension. Furthermore, when the orbit space $\mathbb S^{d-1}/G$ is a Riemannian orbifold, we show that a suitable coorbit filter bank is bi-Lipschitz in the quotient metric.<|reference_end|>
@article{qaddura2024stable,
    title={Stable Coorbit Embeddings of Orbifold Quotients},
    author={Yousef Qaddura, Dustin G. Mixon},
    journal={arXiv preprint arXiv:2403.14042},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.14042},
    primaryClass={math.FA cs.IT math.IT}
}