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dc.contributor.authorNikolov, Geno P.
dc.contributor.authorShadrin, Alexei
dc.date.accessioned2017-05-04T10:59:13Z
dc.date.available2017-05-04T10:59:13Z
dc.date.issued2017-02-22
dc.identifier.urihttps://arxiv.org/abs/1701.07682
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1284
dc.descriptionMSC 2010: 41A17 Key words and phrases: Markov type inequalities, Gegenbauer polynomials, matrix normsen_US
dc.descriptionResearch in Pairs 2016en_US
dc.description.abstractLet $w_{\lambda}(t) := (1-t^2)^{\lambda-1/2}$, where ${\lambda} > -\frac{1}{2}$, 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 $\lambda$.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2017,05
dc.titleOn the Markov inequality in the $L_2$-norm with the Gegenbauer weighten_US
dc.title.alternativeL2en_US
dc.typePreprinten_US
dc.rights.licenseDieses 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.licenseThis 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.doi10.14760/OWP-2017-05
local.scientificprogramResearch in Pairs 2016en_US
local.series.idOWP-2017-05
dc.identifier.urnurn:nbn:de:101:1-201703313724
dc.identifier.ppn165801622X


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