SL(n) covariant matrix-valued valuations on Lp-spaces
Differential Geometry
2024-08-14 v1
Abstract
A complete classification is established for continuous and SL(n) covariant matrix-valued valuations on Lp(Rn,|x|2dx). The assumption of matrix symmetry is eliminated. For n>2, such valuation is uniquely characterized by the moment matrix of measurable function. In the 2-dimensional case, while the rotation matrix shows up.
Cite
@article{arxiv.2408.06835,
title = {SL(n) covariant matrix-valued valuations on Lp-spaces},
author = {Chunna Zeng and Yu Lan},
journal= {arXiv preprint arXiv:2408.06835},
year = {2024}
}