{"paper":{"title":"Two Distinguished Subspaces of Product BMO and the Nehari--AAK Theory for Hankel Operators on the Torus","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Cora Sadosky, Mischa Cotlar","submitted_at":"1995-12-05T00:00:00Z","abstract_excerpt":"In this paper we show that the theory of Hankel operators in the torus $\\T^d$, for $d > 1$, presents striking differences with that on the circle $\\T$, starting with bounded Hankel operators with no bounded symbols. Such differences are circumvented here by replacing the space of symbols $L^\\infty (\\T)$ by BMOr$(\\T^d)$, a subspace of product BMO, and the singular numbers of Hankel operators by so-called sigma numbers. This leads to versions of the Nehari--AAK and Kronecker theorems, and provides conditions for the existence of solutions of product Pick problems through finite Pick-type matrice"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9512212","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"}