Spectral Asymptotics for Quantized Derivatives on Quantum Euclidean Spaces
Functional Analysis
2025-05-20 v1
Abstract
We obtain spectral asymptotics for the quantized derivatives of elements from the first-order homogeneous Sobolev space on the quantum Euclidean space, extending an earlier result of McDonald, Sukochev and Xiong (Commun. Math. Phys. 2020). Our approach is based on a noncommutative Wiener-Ikehara Tauberian theorem and a recently developed -algebraic version of pseudo-differential operator theory.
Cite
@article{arxiv.2505.11789,
title = {Spectral Asymptotics for Quantized Derivatives on Quantum Euclidean Spaces},
author = {Yongqiang Tian},
journal= {arXiv preprint arXiv:2505.11789},
year = {2025}
}