{"paper":{"title":"Analysis of the spectral symbol function for spectral approximation of a differential operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AP"],"primary_cat":"math.NA","authors_text":"Davide Bianchi","submitted_at":"2019-08-15T22:59:40Z","abstract_excerpt":"Given a differential operator $\\mathcal{L}$ along with its own eigenvalue problem $\\mathcal{L}u = \\lambda u$ and an associated algebraic equation $\\mathcal{L}^{(n)} \\mathbf{u}_n = \\lambda\\mathbf{u}_n$ obtained by means of a discretization scheme (like Finite Differences, Finite Elements, Galerkin Isogeometric Analysis, etc.), the theory of Generalized Locally Toeplitz (GLT) sequences serves the purpose to compute the spectral symbol function $\\omega$ associated to the discrete operator $\\mathcal{L}^{(n)}$\n  We prove that the spectral symbol $\\omega$ provides a necessary condition for a discret"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05788","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/1908.05788/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"}