{"paper":{"title":"Hankel and Toeplitz operators: continuous and discrete representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.FA","authors_text":"D. R. Yafaev","submitted_at":"2016-07-18T09:41:09Z","abstract_excerpt":"We find a relation guaranteeing that Hankel operators realized in the space of sequences $\\ell^2 ({\\Bbb Z}_{+}) $ and in the space of functions $L^2 ({\\Bbb R}_{+}) $ are unitarily equivalent. This allows us to obtain exhaustive spectral results for two classes of unbounded Hankel operators in the space $\\ell^2 ({\\Bbb Z}_{+}) $ generalizing in different directions the classical Hilbert matrix. We also discuss a link between representations of Toeplitz operators in the spaces $\\ell^2 ({\\Bbb Z}_{+}) $ and $L^2 ({\\Bbb R}_{+}) $."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04988","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"}