{"paper":{"title":"Extremal functions in de Branges and Euclidean spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Emanuel Carneiro, Friedrich Littmann","submitted_at":"2014-06-20T16:31:30Z","abstract_excerpt":"In this work we obtain optimal majorants and minorants of exponential type for a wide class of radial functions on $\\mathbb{R}^N$. These extremal functions minimize the $L^1(\\mathbb{R}^N, |x|^{2\\nu + 2 - N}dx)$-distance to the original function, where $\\nu >-1$ is a free parameter. To achieve this result we develop new interpolation tools to solve an associated extremal problem for the exponential function $\\mathcal{F}_{\\lambda}(x) = e^{-\\lambda|x|}$, where $\\lambda >0$, in the general framework of de Branges spaces of entire functions. We then specialize the construction to a particular famil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5456","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"}