A Centroid for Sections of a Cube in a Function Space, with application to Colorimetry
Abstract
The definition of the centroid in finite dimensions does not apply in a function space because of the lack of a translation invariant measure. Another approach, suggested by Nik Weaver, is to use a suitable collection of finite-dimensional subspaces. For a specific collection of subspaces of , this approach is shown to be successful when the subset is the intersection of a cube with a closed affine subspace of finite codimension. The techniques used are the classical Laplace Transform and saddlepoint method for asymptotics. Applications to spectral reflectance estimation in colorimetry are presented.
Keywords
Cite
@article{arxiv.1811.00990,
title = {A Centroid for Sections of a Cube in a Function Space, with application to Colorimetry},
author = {Glenn Davis},
journal= {arXiv preprint arXiv:1811.00990},
year = {2020}
}
Comments
41 pages, 10 figures. In v2 revised argument in section 5; the new argument uses the Jordan-Brouwer separation theorem, instead of a global diffeomorphism theorem of Hadamard. In v3 section 5, added two variants of a key lemma. In v4 added remarks about the Langevin function, and more references