{"paper":{"title":"Nehari's theorem for convex domain Hankel and Toeplitz operators in several variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Karl-Mikael Perfekt, Marcus Carlsson","submitted_at":"2017-09-06T14:44:42Z","abstract_excerpt":"We prove Nehari's theorem for integral Hankel and Toeplitz operators on simple convex polytopes in several variables. A special case of the theorem, generalizing the boundedness criterion of the Hankel and Toeplitz operators on the Paley-Wiener space, reads as follows. Let $\\Xi = (0,1)^d$ be a $d$-dimensional cube, and for a distribution $f$ on $2\\Xi$, consider the Hankel operator\n  $$\\Gamma_f (g)(x)=\\int_{\\Xi} f(x+y) g(y) \\, dy, \\quad x \\in\\Xi.$$ Then $\\Gamma_f$ extends to a bounded operator on $L^2(\\Xi)$ if and only if there is a bounded function $b$ on $\\mathbb{R}^d$ whose Fourier transform"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01843","kind":"arxiv","version":3},"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"}