{"paper":{"title":"On Strong Markushevich bases $\\{t^{\\lambda_n}\\}_{n=1}^{\\infty}$ in their closed span in $L^2 (0, 1)$ and characterizing a subspace of $H^2 (\\mathbb{D})$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Elias Zikkos","submitted_at":"2025-05-30T16:20:25Z","abstract_excerpt":"Let $\\Lambda=\\{\\lambda_n\\}_{n=1}^{\\infty}$ be a strictly increasing sequence of positive real numbers such that $\\sum_{n=1}^{\\infty}\\frac{1}{\\lambda_n}<\\infty$ and $\\inf(\\lambda_{n+1}-\\lambda_n)>0$. We investigate properties of the closed span of the system $\\{t^{\\lambda_n}\\}_{n=1}^{\\infty}$ in $L^2 (0,1)$, denoted by $\\overline{M_{\\Lambda}}$, and of the unique biorthogonal family $\\{r_n (t)\\}_{n=1}^{\\infty}$ to the system $\\{t^{\\lambda_n}\\}_{n=1}^{\\infty}$ in $\\overline{M_{\\Lambda}}$. We show that the system $\\{t^{\\lambda_n}\\}_{n=1}^{\\infty}$ is a strong Markushevich basis in $\\overline{M_{\\L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24761","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/2505.24761/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"}