{"paper":{"title":"Hilbert-Schmidt and Trace Class Pseudo-differential Operators on the Abstract Heisenberg Group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Aparajita Dasgupta, Vishvesh Kumar","submitted_at":"2019-02-26T11:24:40Z","abstract_excerpt":"In this paper we introduce and study pseudo-differential operators with operator valued symbols on the abstract Heisenberg group $\\mathbb{H}(G):=G \\times \\widehat{G} \\times \\mathbb{T},$ where $G$ a locally compact abelian group with its dual group $\\widehat{G}$. We obtain a necessary and sufficient condition on symbols for which these operators are in the class of Hilbert-Schmidt operators. As a key step in proving this we derive a trace formula for the trace class $j$-Weyl transform, $j \\in \\mathbb{Z}^*$ with symbols in $L^{2}(G\\times \\widehat{G}).$ We go on to present a characterization of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09869","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}