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arXiv · 2408.06835

SL(n) covariant matrix-valued valuations on Lp-spaces

Chunna Zeng·Yu Lan
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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.

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Chunna Zeng, Yu Lan. 2024-08-13. SL(n) covariant matrix-valued valuations on Lp-spaces. https://arxiv.org/abs/2408.06835

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