{"paper":{"title":"Continuous Gabor transform for semi-direct product of locally compact groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Arash Ghaani Farashahi","submitted_at":"2012-03-07T16:13:45Z","abstract_excerpt":"Let $H$ be a locally compact group, $K$ be an LCA group, $\\tau:H\\to Aut(K)$ be a continuous homomorphism and $G_\\tau=H\\ltimes_\\tau K$ be the semi-direct product of $H$ and $K$ with respect to the continuous homomorphism $\\tau$. In this article we introduce the $\\tau\\times\\hat{\\tau}$-time frequency group $G_{\\tau\\times\\hat{\\tau}}$. We define the $\\tau\\times\\hat{\\tau}$-continuous Gabor transform of $f\\in L^2(G_\\tau)$ with respect to a window function $u\\in L^2(K)$ as a function defined on $G_{\\tau\\times\\hat{\\tau}}$. It is also shown that the $\\tau\\times\\hat{\\tau}$-continuous Gabor transform sati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1517","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"}