{"paper":{"title":"General theory of regular biorthogonal pairs and its physical applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"H. Inoue","submitted_at":"2016-04-07T12:11:19Z","abstract_excerpt":"In this paper we introduce a general theory of regular biorthogonal sequences and its physical applications. Biorthogonal sequences $\\{ \\phi_{n} \\}$ and $\\{ \\psi_{n} \\}$ in a Hilbert space ${\\cal H}$ are said to be regular if $Span\\; \\{ \\phi_{n} \\}$ and $Span\\; \\{ \\psi_{n} \\}$ are dense in ${\\cal H}$. The first purpose is to show that there exists a non-singular positive self-adjoint operator $T_{\\mbox{$f$}}$ in ${\\cal H}$ defined by an ONB $\\mbox{$f$} \\equiv \\{ f_{n} \\}$ in ${\\cal H}$ such that $\\phi_{n}=T_{\\mbox{$f$}} f_{n}$ and $\\psi_{n}= T_{\\mbox{$f$}}^{-1} f_{n}$, $n=0,1, \\cdots$, and suc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01967","kind":"arxiv","version":4},"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"}