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

2019/11/24 by Vishvesh Kumar, Shyam Swarup Mondal, Kumar, Vishvesh +1
Mathematics · #35S05 #43A85 (Secondary) #47G30 (Primary) #Advanced Algebra and Geometry #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1911.10554

openalex publication_date 2019/11/24 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

Given a compact (Hausdorff) group G and a closed subgroup H of G, in\nthis paper we present symbolic criteria for pseudo-differential operators on\ncompact homogeneous space G/H characterizing the Schatten-von Neumann classes\nS_r(L²(G/H)) for all 0<r \≤ \∞. We go on to provide a symbolic\ncharacterization for r-nuclear, 0< r \≤ 1, pseudo-differential operators\non L^p(G/H)-space with applications to adjoint, product and trace formulae.\nThe criteria here are given in terms of the concept of matrix-valued symbols\ndefined on noncommutative analogue of phase space G/H \× widehatG/H.\nFinally, we present applications of aforementioned results in the context of\nheat kernels.\n

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