论文标题
量子衍生物的奇异值的渐近学
Asymptotics of singular values for quantum derivatives
论文作者
论文摘要
我们从homgeneous sobolev space $ \ dot {w}^1_d（\ mathbb {r}^d）$ on $ \ mathbb {r}^d。 f \ | _ {l_d（\ Mathbb r^d）} $等同于主要的$ \ dbar f $在主要的理想$ \ mathcal {l} _ {d，\ infty}，$因此，提供了一个非敏感的，均匀的，基于$ \ dbar f。 $ c^{\ ast} $ - $ \ mathbb {r}^d $上的主要符号映射的代数概念，这是最近两位作者和合作者最近开发的。
We obtain Weyl type asymptotics for the quantised derivative $\dbar f$ of a function $f$ from the homgeneous Sobolev space $\dot{W}^1_d(\mathbb{R}^d)$ on $\mathbb{R}^d.$ The asymptotic coefficient $\|\nabla f\|_{L_d(\mathbb R^d)}$ is equivalent to the norm of $\dbar f$ in the principal ideal $\mathcal{L}_{d,\infty},$ thus, providing a non-asymptotic, uniform bound on the spectrum of $\dbar f.$ Our methods are based on the $C^{\ast}$-algebraic notion of the principal symbol mapping on $\mathbb{R}^d$, as developed recently by the last two authors and collaborators.
