Stable Coorbit Embeddings of Orbifold Quotients
CoRR(2024)
摘要
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=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 𝕊^d-1/G is a Riemannian orbifold, we show that
a suitable coorbit filter bank is bi-Lipschitz in the quotient metric.
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