{"paper":{"title":"Closed form solution of non-homogeneous equations with Toeplitz plus Hankel operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Bernd Silbermann, Victor D. Didenko","submitted_at":"2015-02-28T01:22:28Z","abstract_excerpt":"Considered is the equation\n  $$\n  (T(a)+H(b))\\phi=f,\n  $$ where $T(a)$ and $H(b)$, $a,b\\in L^\\infty(\\mathbb{T})$ are, respectively, Toeplitz and Hankel operators acting on the classical Hardy spaces $H^p(\\mathbb{T})$, $1<p<\\infty$. If the generating functions $a$ and $b$ satisfy the so-called matching condition [1,2],\n  $$ a(t) a(1/t)=b(t)b(1/t), \\, t\\in \\mathbb{T},\n  $$ an efficient method for solving equations with Toeplitz plus Hankel operators is proposed. The method is based on the Wiener--Hopf factorization of the scalar functions $c(t)=a(t)b^{-1}(t)$ and $d(t)=a(t)b^{-1}(1/t)$ and allow"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00050","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"}