{"paper":{"title":"Tempered distributions and Fourier transform on the Heisenberg group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Hajer Bahouri (LAMA), Jean-Yves Chemin (LJLL), Raphael Danchin","submitted_at":"2017-05-05T12:48:48Z","abstract_excerpt":"The final goal of the present work is to  extend the Fourier  transform on the Heisenberg group $\\H^d,$ to tempered distributions.  As in  the Euclidean setting, the strategy is to first show that the Fourier transform is an isomorphism on the Schwartz space, then to define the extension by duality. The difficulty that is here encountered  is that the Fourier transform of an integrable function on $\\H^d$is no  longer a function on $\\H^d$ : according to the standard definition, it is a family of bounded operators on  $L^2(\\R^d).$ Following our new approach in\\ccite{bcdFHspace}, we here define t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02195","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"}