Asymptotics of singular values for quantised derivatives on noncommutative tori
Asymptotics of singular values for quantised derivatives on noncommutative tori
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DOI：
10.1016/j.jfa.2023.110021
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发表时间：
2023-05
影响因子：
1.7
通讯作者：
F. Sukochev;Xiaolei Xiong;D. Zanin
中科院分区：
文献类型：
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作者：
F. Sukochev;Xiaolei Xiong;D. Zanin
我们得到了形式为T I θ− 1的量子环面T θ d上伪微分算子的Weyl型渐近性。这里T代表0阶量子环面上的经典伪微分算子，I θ− 1是− 1阶的Riesz势。作为应用，我们得到了算子x在齐次Sobolev空间Wstecd 1（T θ d）上的量子化导数Image 1的Weyl型渐近性.渐近系数等价于主理想L d，∞中图像1的范数以及W stecd 1（T θ d）中x的范数。我们精确并纠正了我们之前关于图像1的量子积分公式的论文（Comm. Math. Phys. 371（2019），no. 3，1231-1260）中的早期结果。
We obtain Weyl type asymptotics for pseudodifferential operators on quantum torus T θ d of the form T I θ− 1. Here T stands for classical pseudodifferential operators on quantum torus of order 0, and I θ− 1 is the Riesz potential of order− 1. As an application, we obtain Weyl type asymptotics for the quantised derivative Image 1 of an operator x from the homogeneous Sobolev space W˙ d 1 (T θ d). The asymptotic coefficient is equivalent to the norm of Image 1 in the principal ideal L d,∞, as well as the norm of x in W˙ d 1 (T θ d). We precise and rectify earlier results in our previous paper (Comm. Math. Phys. 371 (2019), no. 3, 1231–1260) on quantum integration formula for Image 1.