{"paper":{"title":"An index formula in connection with meromorphic approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV"],"primary_cat":"math.FA","authors_text":"Alberto A. Condori","submitted_at":"2011-03-21T00:22:22Z","abstract_excerpt":"Let $\\Phi$ be a continuous $n\\times n$ matrix-valued function on the unit circle $\\T$ such that the $(k-1)$th singular value of the Hankel operator with symbol $\\Phi$ is greater than the $k$th singular value. In this case, it is well-known that $\\Phi$ has a unique superoptimal meromorphic approximant $Q$ in $H^{\\infty}_{(k)}$; that is, $Q$ has at most $k$ poles in the unit disc $\\mathbb{D}$ (i.e. the McMillan degree of $Q$ in $\\mathbb{D}$ is at most $k$) and $Q$ minimizes the essential suprema of singular values $s_{j}((\\Phi-Q)(\\zeta))$, $j\\geq0$, with respect to the lexicographic ordering. Fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3906","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"}