Asymptotics of the best polynomial approximation of $|x|^p$ and of the best Laurent polynomial approximation of $\sgn(x)$ on two symmetric intervals

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dc.creatorNazarov, F.
dc.creatorPeherstorfer, F.
dc.creatorVolberg, A.
dc.creatorYuditskii, P.
dc.date2009-03-21
dc.date.accessioned2026-07-07T12:55:31Z
dc.date.available2026-07-07T12:55:31Z
dc.descriptionWe present a new method that allows us to get a direct proof of the classical Bernstein asymptotics for the error of the best uniform polynomial approximation of $|x|^p$ on two symmetric intervals. Note, that in addition, we get asymptotics for the polynomials themselves under a certain renormalization. Also, we solve a problem on asymptotics of the best approximation of $\sgn(x)$ on $[-1,-a]\cup[a,1]$ by Laurent polynomials.
dc.identifierhttps://arxiv.org/abs/0903.3652
dc.identifierhttp://arxiv.org/abs/0903.3652
dc.identifierConstr. Approx. (2009) 29; 23-39
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/224276
dc.subjectClassical Analysis and ODEs
dc.subjectComplex Variables
dc.titleAsymptotics of the best polynomial approximation of $|x|^p$ and of the best Laurent polynomial approximation of $\sgn(x)$ on two symmetric intervals
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