PreprintCC BY 4.0arXiv
Tensor valuations on Sobolev spaces
Abstract
A complete classification is established for continuous, SL(n) contravariant, and translation invariant tensor valuations defined on the Sobolev space W1,p(ℝn). When these valuations are further assumed to be homogeneous, the classification reveals that they are precisely the Fisher information tensors, which constitute a higher-order generalization of the Fisher information matrix.
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BibTeX
@misc{gao2026tensor,
title = {{Tensor valuations on Sobolev spaces}},
author = {Tian Gao and Dan Ma},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37580},
eprint = {2609.37580},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37580},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Tensor valuations on Sobolev spaces
AU - Tian Gao
AU - Dan Ma
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37580
UR - https://arxiv.org/abs/2609.37580
AB - A complete classification is established for continuous, SL(n) contravariant, and translation invariant tensor valuations defined on the Sobolev space W^1,p(ℝ^n). When these valuations are further assumed to be homogeneous, the classification reveals that they are precisely the Fisher information tensors, which constitute a higher-order generalization of the Fisher information matrix.
ER -