{"paper":{"title":"Passive approximation and optimization using B-splines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Annemarie Luger, B. L. G. Jonsson, B\\\"orje Nilsson, Joachim Toft, Mats Gustafsson, Sven Nordebo, Yevhen Ivanenko","submitted_at":"2017-11-20T11:09:34Z","abstract_excerpt":"A passive approximation problem is formulated where the target function is an arbitrary complex valued continuous function defined on an approximation domain consisting of a finite union of closed and bounded intervals on the real axis. The norm used is a weighted $\\text{L}^p$-norm where $1\\leq p\\leq\\infty$. The approximating functions are Herglotz functions generated by a measure with H\\\"{o}lder continuous density in an arbitrary neighborhood of the approximation domain. Hence, the imaginary and the real parts of the approximating functions are H\\\"{o}lder continuous functions given by the den"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07937","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"}