{"paper":{"title":"On the $L_2$ Markov Inequality with Laguerre Weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexei Shadrin, Geno Nikolov","submitted_at":"2016-05-09T10:31:19Z","abstract_excerpt":"Let $w_{\\alpha}(t)=t^{\\alpha}\\,e^{-t}$, $\\alpha>-1$, be the Laguerre weight function, and $|\\cdot|_{w_\\alpha}$ denote the associated $L_2$-norm, i.e., $$ | f|_{w_\\alpha}:=\\Big(\\int_{0}^{\\infty}w_{\\alpha}(t)| f(t)|^2\\,dt\\Big)^{1/2}. $$ Denote by ${\\cal P}_n$ the set of algebraic polynomials of degree not exceeding $n$. We study the best constant $c_n(\\alpha)$ in the Markov inequality in this norm, $$ | p^{\\prime}|_{w_\\alpha}\\leq c_n(\\alpha)\\,| p|_{w_\\alpha}\\,,\\quad p\\in {\\cal P}_n\\,, $$ namely the constant $$ c_{n}(\\alpha)=\\sup_{\\mathop{}^{p\\in {\\cal P}_n}_{p\\ne 0}}\\frac{| p^{\\prime}|_{w_\\alpha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02508","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"}