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Injectivity, stability, and positive definiteness of max filtering

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arxiv 2212.11156 v2 pith:R3B6BZWW submitted 2022-12-21 math.FA cs.ITmath.IT

Dustin G. Mixon , Yousef Qaddura This is my paper · ORCID
classification math.FAcs.ITmath.IT
keywords filteringspacemapspositivewhencharacterizeclassconditions
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Given a real inner product space V and a group G of linear isometries, max filtering offers a rich class of G-invariant maps. In this paper, we identify nearly sharp conditions under which these maps injectively embed the orbit space V/G into Euclidean space, and when G is finite, we estimate the map's distortion of the quotient metric. We also characterize when max filtering is a positive definite kernel.

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  1. Recovering a group from few orbits

    math.RT 2024-11 conditional novelty 7.0 of 10

    One generic complex orbit determines a finite linear symmetry group up to isomorphism; two generic real orbits suffice, and concrete recovery needs an orbit count governed by representation multiplicities.

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