{"paper":{"title":"Approximation by amplitude and frequency operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Petr Chunaev, Vladimir Danchenko","submitted_at":"2014-09-15T09:20:42Z","abstract_excerpt":"We study Pad\\'{e} interpolation at the node $z=0$ of functions $f(z)=\\sum_{m=0}^{\\infty} f_m z^m$, analytic in a neighbourhood of this node, by amplitude and frequency operators (sums) of the form $$\n  \\sum_{k=1}^n \\mu_k h(\\lambda_k z), \\qquad \\mu_k,\\lambda_k\\in \\mathbb{C}. $$ Here $h(z)=\\sum_{m=0}^{\\infty} h_m z^m$, $h_m\\ne 0$, is a fixed (basis) function, analytic at the origin, and the interpolation is carried out by an appropriate choice of amplitudes $\\mu_k $ and frequencies $\\lambda_k$. The solvability of the $2n$-multiple interpolation problem is determined by the solvability of the ass"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4188","kind":"arxiv","version":3},"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"}