{"paper":{"title":"A mapping defined by the Schur-Szeg\\H{o} composition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Vladimir Petrov Kostov","submitted_at":"2015-04-08T09:08:51Z","abstract_excerpt":"Each degree $n+k$ polynomial of the form $(x+1)^k(x^n+c_1x^{n-1}+\\cdots +c_n)$, $k\\in \\mathbb{N}$, is representable as Schur-Szeg\\H{o} composition of $n$ polynomials of the form $(x+1)^{n+k-1}(x+a_j)$. We study properties of the affine mapping $\\Phi _{n,k}$~:~$(c_1,\\ldots ,c_n)$ $\\mapsto$ $(\\sigma _1, \\ldots ,\\sigma _n)$, where $\\sigma _i$ are the elementary symmetric polynomials of the numbers $a_j$. We study also properties of a similar mapping for functions of the form $e^xP$, where $P$ is a polynomial, $P(0)=1$, and we extend the Descartes rule to them."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01870","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"}