{"paper":{"title":"Orthogonal projectors onto spaces of periodic splines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Markus Passenbrunner","submitted_at":"2016-08-24T05:48:46Z","abstract_excerpt":"The main result of this paper is a proof that for any integrable function $f$ on the torus, any sequence of its orthogonal projections $(\\widetilde{P}_n f)$ onto periodic spline spaces with arbitrary knots $\\widetilde{\\Delta}_n$ and arbitrary polynomial degree converges to $f$ almost everywhere with respect to the Lebesgue measure, provided the mesh diameter $|\\widetilde{\\Delta}_n|$ tends to zero. We also give a proof of the fact that the operators $\\widetilde{P}_n$ are bounded on $L^\\infty$ independently of the knots $\\widetilde{\\Delta}_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06720","kind":"arxiv","version":2},"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"}