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- W4315706679 abstract "Let $G$ be a compact Lie group of dimension $n.$ In this work we characterise the membership of classical pseudo-differential operators on $G$ in the trace class ideal $S_{1}(L^2(G)),$ as well as in the setting of the Schatten ideals $S_{r}(L^2(G)),$ for all $r>0.$ In particular, we deduce Schatten characterisations of elliptic pseudo-differential operators of $(rho,delta)$-type for the large range $0leq delta<rholeq 1.$ Additional necessary and sufficient conditions are given in terms of the matrix-valued symbols of the operators, which are global functions on the phase space $Gtimes widehat{G},$ with the momentum variables belonging to the unitary dual $widehat{G}$ of $G$. In terms of the parameters $(rho,delta),$ on the torus $mathbb{T}^n,$ we demonstrate the sharpness of our results showing the existence of atypical operators in the exotic class $Psi^{-varkappa}_{0,0}(mathbb{T}^n),$ $varkappa>0,$ belonging to all the Schatten ideals. Additional order criteria are given in the setting of classical pseudo-differential operators. We present also some open problems in this setting." @default.
- W4315706679 created "2023-01-12" @default.
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- W4315706679 date "2023-01-10" @default.
- W4315706679 modified "2023-09-23" @default.
- W4315706679 title "Schatten-von Neumann properties for Hormander classes on compact Lie groups" @default.
- W4315706679 doi "https://doi.org/10.48550/arxiv.2301.04044" @default.
- W4315706679 hasPublicationYear "2023" @default.
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