Year: 2025
Type: preprint
Abstract: Let $(X,G)$ be a $d$-dimensional compact smooth Riemannian manifold equipped with Laplace-Beltrami operator $Δ_{G}$, and let $Π_{X}$ be the $C^{\ast}$-algebra obtained by locally transferring the $C^{\ast}$-algebra generated by multiplication operators and Riesz transforms on $\mathbb{R}^{d}$. Denote ${\rm sym}_{X}$ the principal symbol mapping of $Π_{X}$. For any $S\inΠ_{X}$, we prove that, in the framework of $C^{\ast}$-algebra, \begin{align*} \lim_{t\rightarrow\infty}t^{\frac{1}{p}}μ(t,S(1+Δ_G)^{-\frac{d}{2p}}) =(2π\sqrt[d]{d})^{-\frac{1}{p}}\Big\|{\rm sym}_{X}(S)\Big\|_{L_{p}(T^{\ast}X,e^{-q_{G}}dλ)}, \end{align*} where $0
Source: arXiv (Cornell University)
Authors: Sukochev, Fedor, Yang, Fulin, Zanin, Dmitriy
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417005402
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