{"paper":{"title":"A new approach to the Fourier analysis on semi-direct products of groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.FA","authors_text":"Arash Ghaani Farashahi","submitted_at":"2012-01-05T14:36:31Z","abstract_excerpt":"Let $H$ and $K$ be locally compact groups and also $\\tau:H\\to Aut(K)$ 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 $\\tau$. This paper presents a novel approach to the Fourier analysis of $G_\\tau$, when $K$ is abelian. We define the $\\tau$-dual group $G_{\\hat{\\tau}}$ of $G_\\tau$ as the semi-direct product $H\\ltimes_{\\hat{\\tau}}\\hat{K}$, where $\\hat{\\tau}:H\\to Aut(\\hat{K})$ defined via (\\ref{A}). We prove a Ponterjagin duality Theorem and also we study $\\tau$-Fourier transforms on $G_\\tau$. As a co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1179","kind":"arxiv","version":2},"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"}