{"paper":{"title":"Uniformly bounded orthonormal polynomials on the sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Joaquim Ortega-Cerd\\`a, Jordi Marzo","submitted_at":"2014-05-21T13:36:50Z","abstract_excerpt":"Given any $\\varepsilon>0$, we construct an orthonormal system of $n_k$ uniformly bounded polynomials of degree at most $k$ on the unit sphere in $\\mathbb R^{m+1}$ where $n_k$ is bigger than $1-\\varepsilon$ times the dimension of the space of polynomials of degree at most $k$. Similarly we construct an orthonormal system of sections of powers $L^k$ of a positive holomorphic line bundle on a compact K\\\"ahler manifold with cardinality bigger than $1-\\varepsilon$ times the dimension of the space of global holomorphic sections to $L^k$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5417","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"}