Quantum differentiability on noncommutative Euclidean spaces

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 $0<\alpha \le \frac{1}{d}$. This result is substantially more difficult than the analogous problems for Euclidean space and for quantum $d$-tori.

arXiv commentAccepted to Comm. Math. Phys

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Cited by in corpus (4)

• Sharp estimates of noncommutative Bochner-Riesz means on two-dimensional quantum tori
• Fourier multipliers and their applications to PDE on the quantum Euclidean space
• Sobolev inequality and its applications to nonlinear PDE on noncommutative Euclidean spaces
• $L^p-L^q$ boundedness of Fourier multipliers on quantum Euclidean spaces