{"paper":{"title":"The Weyl calculus for group generators satisfying the canonical commutation relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.FA","authors_text":"Jan van Neerven, Pierre Portal","submitted_at":"2018-06-04T06:49:11Z","abstract_excerpt":"Classical pseudo-differential calculus on $\\mathbb{R}^{d}$ can be viewed as a (non-commutative) functional calculus for the standard position and momentum operators $(Q_{1}, \\dots , Q_{d})$ and $(P_{1}, \\dots , P_{d})$. We generalise this calculus to the setting of two $d$-tuples of operators $A=(A_{1}, \\dots , A_{d})$ and $B=(B_{1}, \\dots , B_{d})$ acting on a Banach space $X$ such that $iA_{1}, \\dots , iA_{d}$ and $iB_{1}, \\dots , iB_{d}$ generate bounded $C_0$-groups satisfying the Weyl canonical commutation relations $e^{isA_j}e^{itA_k} = e^{itA_k}e^{isA_j}$, $e^{isB_j}e^{itB_k} = e^{itB_k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00980","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"}