A Centroid for Sections of a Cube in a Function Space, with application to Colorimetry
arXiv:1811.00990
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.
arXiv comment41 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