Approximating a norm by a polynomial

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dc.creatorBarvinok, Alexander
dc.date2001-05-09
dc.date.accessioned2026-07-07T04:41:37Z
dc.date.available2026-07-07T04:41:37Z
dc.descriptionWe prove that for any norm |*| in the d-dimensional real vector space V and for any odd n>0 there is a non-negative polynomial p(x), x in V of degree 2n such that p^{1/2n}(x) < |x| < c(n,d) p^{1/2n}(x), where c(n,d)={n+d-1 choose n}^{1/2n}. Corollaries and polynomial approximations of the Minkowski functional of a convex body are discussed.
dc.description5 pages
dc.identifierhttps://arxiv.org/abs/math/0105069
dc.identifierhttp://arxiv.org/abs/math/0105069
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61437
dc.subjectFunctional Analysis
dc.subjectMetric Geometry
dc.subject46B07 68W25
dc.titleApproximating a norm by a polynomial
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