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= Rᵈ 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 Sᵈ⁻¹/G is a Riemannian orbifold, we show that a suitable coorbit filter bank is bi-Lipschitz in the quotient metric.