{"paper":{"title":"The Bender-Dunne basis operators as Hilbert space operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Eric Galapon, Joseph Bunao","submitted_at":"2015-09-01T15:09:19Z","abstract_excerpt":"The Bender-Dunne basis operators, $\\mathsf{T}_{-m,n}=2^{-n}\\sum_{k=0}^n {n \\choose k} \\mathsf{q}^k \\mathsf{p}^{-m} \\mathsf{q}^{n-k}$ where $\\mathsf{q}$ and $\\mathsf{p}$ are the position and momentum operators respectively, are formal integral operators in position representation in the entire real line $\\mathbb{R}$ for positive integers $n$ and $m$. We show, by explicit construction of a dense domain, that the operators $\\mathsf{T}_{-m,n}$'s are densely defined operators in the Hilbert space $L^2(\\mathbb{R})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00340","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"}