{"paper":{"title":"Spaces of polynomial functions of bounded degrees on an embedded manifold and their duals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Shuzo Izumi","submitted_at":"2011-02-14T16:12:05Z","abstract_excerpt":"Let $\\mathcal{O}(U)$ denote the algebra of holomorphic functions on an open subset $U\\subset\\mathbb{C}^n$ and $Z\\subset\\mathcal{O}(U)$ its finite-dimensional vector subspace. By the theory of least space of de Boor and Ron, there exists a projection $T_b$ from the local ring $\\mathcal{O}_{n,b}$ onto the space $Z_b$ of germs of elements of $Z$ at $b$. At general $b\\in U$, its kernel is an ideal and induces a structure of an Artinian algebra on $Z_b$. In particular, it holds at points where $k$-th jets of elements of $Z$ form a vector bundle for each $k\\le\\dim_{\\mathbb{C}}Z_b-1$. Using $T_b$ we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2813","kind":"arxiv","version":8},"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"}