{"paper":{"title":"Generalized Toeplitz plus Hankel operators: kernel structure and defect numbers","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":"2015-01-18T08:12:16Z","abstract_excerpt":"Generalized Toeplitz plus Hankel operators $T(a)+H_{\\alpha}(b)$ generated by functions $a,b$ and a linear fractional Carleman shift $\\alpha$ changing the orientation of the unit circle $\\mathbb{T}$ are considered on the Hardy spaces $H^p(\\mathbb{T})$, $1<p<\\infty$. If the functions $a,b\\in L^\\infty(\\mathbb{T})$ and satisfy the condition\n  $$ a(t) a(\\alpha(t))=b(t) b(\\alpha(t)),\\quad t\\in \\mathbb{T}, $$ the defect numbers of the operators $T(a)+H_{\\alpha}(b)$ are established and an explicit description of the structure of the kernels and cokernels of the operators mentioned is given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04271","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"}