2024/08/13 by Chunna Zeng, Zeng, Chunna, Yu Lan +1
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces
paper · pdf · doi:10.48550/arxiv.2408.06835
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.