{"paper":{"title":"Topological analysis in $\\mathcal{R}(p,q)-$anisotropic sector and nuclear space on $\\mathcal{R}(p,q)-$quantum deformed algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.QA","authors_text":"Isiaka Aremua, Joseph D\\'esir\\'e Bukweli Kyemba, Kaw\\`eyim Lankpetre","submitted_at":"2026-05-19T18:44:57Z","abstract_excerpt":"The purpose of this article is to develop and analyze $\\mathcal{R}(p,q)-$topological analysis of the classical nuclear space within the general framework of $\\mathcal{R}(p,q)-$calculus. We begin by introducing the $\\mathcal{R}(p,q)-$Gamma functions, establishing their main properties and their connection with the deformed factorials. We develop a rigorous analytic and functional-analytic framework for holomorphic functions governed by a general $\\mathcal{R}(p,q)-$deformation, where $\\mathcal{R}(u,v)$ is a meromorphic kernel satisfying $0<q<p\\leq 1$, $\\mathcal{R}(1,1)=0$, and $\\mathcal{R}(p^n,q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24010","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.24010/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}