{"paper":{"title":"Dimension elevation in Muntz spaces: A new emergence of the Muntz condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Rachid Ait-Haddou","submitted_at":"2013-09-04T08:08:37Z","abstract_excerpt":"We show that the limiting polygon generated by the dimension elevation algorithm with respect to the \\muntz space $span(1,t^{r_1},t^{r_2},...,t^{r_m},...)$, with $0 < r_1 < r_2 < ... < r_m < ...$ and $\\lim_{n\\to\\infty}r_n = \\infty$, over an interval $[a,b]\\subset]0,\\infty[$ converges to the underlying Chebyshev-B\\'ezier curve if and only if the \\muntz condition $\\sum_{i=1}^{\\infty} \\frac{1}{r_i} = \\infty$ is satisfied. The surprising emergence of the \\muntz condition in the problem raises the question of a possible connection between the density questions of nested Chebyshev spaces and the con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0938","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":""},"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"}