dc.contributor.author Nikolov, Geno P. dc.contributor.author Shadrin, Alexei dc.date.accessioned 2017-05-04T10:59:13Z dc.date.available 2017-05-04T10:59:13Z dc.date.issued 2017-02-22 dc.identifier.uri https://arxiv.org/abs/1701.07682 dc.identifier.uri http://publications.mfo.de/handle/mfo/1284 dc.description MSC 2010: 41A17 en_US Key words and phrases: Markov type inequalities, Gegenbauer polynomials, matrix norms dc.description Research in Pairs 2016 en_US dc.description.abstract Let $w_{\lambda}(t) := (1-t^2)^{\lambda-1/2}$, where ${\lambda} > en_US -\frac{1}{2}$, be the Gegenbauer weight function, let $\|\cdot\|_{w_{\lambda}}$ be the associated $L_2$-norm, $$|f\|_{w_{\lambda}} = \left\{\int_{-1}^1 |f(x)|^2 w_{\lambda}(x)\,dx\right\}^{1/2}\,,$$ and denote by $\mathcal{P}_n$ the space of algebraic polynomials of degree $\le n$. We study the best constant $c_n(\lambda)$ in the Markov inequality in this norm $$\|p_n'\|_{w_{\lambda}} \le c_n(\lambda) \|p_n\|_{w_{\lambda}}\,,\qquad p_n \in \mathcal{P}_n\,,$$ namely the constant $$c_n(\lambda) := \sup_{p_n \in \mathcal{P}_n} \frac{\|p_n'\|_{w_{\lambda}}}{\|p_n\|_{w_{\lambda}}}\,.$$ We derive explicit lower and upper bounds for the Markov constant $c_n(\lambda)$, which are valid for all $n$ and $\lambda$. dc.language.iso en en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2017,05 dc.title On the Markov inequality in the $L_2$-norm with the Gegenbauer weight en_US dc.title.alternative L2 en_US dc.type Preprint en_US dc.rights.license Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. de dc.rights.license This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. en dc.identifier.doi 10.14760/OWP-2017-05 local.scientificprogram Research in Pairs 2016 en_US local.series.id OWP-2017-05 dc.identifier.urn urn:nbn:de:101:1-201703313724 dc.identifier.ppn 165801622X
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