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arXiv · 1911.10554

Schatten Class and nuclear pseudo-differential operators on homogeneous spaces of compact groups

Vishvesh Kumar·Shyam Swarup Mondal
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Abstract

Given a compact (Hausdorff) group $G$ and a closed subgroup $H$ of $G,$ in this paper we present symbolic criteria for pseudo-differential operators on compact homogeneous space $G/H$ characterizing the Schatten-von Neumann classes $S_r(L^2(G/H))$ for all $0<r \leq \infty.$ We go on to provide a symbolic characterization for $r$-nuclear, $0< r \leq 1,$ pseudo-differential operators on $L^{p}(G/H)$-space with applications to adjoint, product and trace formulae. The criteria here are given in terms of the concept of matrix-valued symbols defined on noncommutative analogue of phase space $G/H \times \widehat{G/H}.$ Finally, we present applications of aforementioned results in the context of heat kernels.

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Vishvesh Kumar, Shyam Swarup Mondal. 2019-11-24. Schatten Class and nuclear pseudo-differential operators on homogeneous spaces of compact groups. https://arxiv.org/abs/1911.10554

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