{"paper":{"title":"A functional model for the Fourier--Plancherel operator truncated on the positive half-axis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Victor Katsnelson","submitted_at":"2017-10-30T08:46:59Z","abstract_excerpt":"The truncated Fourier operator $\\mathscr{F}_{\\mathbb{R^{+}}}$, $$ (\\mathscr{F}_{\\mathbb{R^{+}}}x)(t)=\\frac{1}{\\sqrt{2\\pi}} \\int\\limits_{\\mathbb{R^{+}}}x(\\xi)e^{it\\xi}\\,d\\xi\\,,\\ \\ \\ t\\in{}{\\mathbb{R^{+}}}, $$ is studied. The operator $\\mathscr{F}_{\\mathbb{R^{+}}}$ is considered as an operator acting in the space $L^2(\\mathbb{R^{+}})$. The functional model for the operator $\\mathscr{F}_{\\mathbb{R^{+}}}$ is constructed. This functional model is the multiplication operator on the appropriate $2\\times2$ matrix function acting in the space $L^2(\\mathbb{R^{+}})\\oplus{}L^2(\\mathbb{R^{+}})$. Using this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11494","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"}