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arXiv · 1909.03581

Quantum differentiability on noncommutative Euclidean spaces

Edward McDonald·Fedor Sukochev·Xiao Xiong
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Abstract

We study the topic of quantum differentiability on quantum Euclidean $d$-dimensional spaces (otherwise known as Moyal $d$-spaces), and we find conditions that are necessary and sufficient for the singular values of the quantised differential to have decay $O(n^{-\alpha})$ for $0 < \alpha \leq \frac{1}{d}$. This result is substantially more difficult than the analogous problems for Euclidean space and for quantum $d$-tori.

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Edward McDonald, Fedor Sukochev, Xiao Xiong. 2019-09-09. Quantum differentiability on noncommutative Euclidean spaces. https://doi.org/10.1007/s00220-019-03605-2

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