{"paper":{"title":"Semi-regular biorthogonal pairs and generalized Riesz bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Hiroshi Inoue","submitted_at":"2016-08-14T02:24:48Z","abstract_excerpt":"In this paper we define the notion of semi-regular biorthogonal pairs what is a generalization of regular biorthogonal pairs in Ref. \\cite{hiroshi1} and show that if $(\\{ \\phi_{n} \\} , \\{ \\psi_{n} \\})$ is a semi-regular biorthogonal pair, then $\\{ \\phi_{n} \\}$ and $\\{ \\psi_{n} \\}$ are generalized Riesz bases. This result improves the results of Ref. \\cite{h-t, hiroshi1, h-t2} in the regular case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04050","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"}