Approximating a norm by a polynomial

Details Approximating a norm by a polynomial Approximating a norm by a polynomial

2001-05-09

arxiv.org/abs/math/0105069v1

Mathematics

Functional Analysis

5 pages

Scientific paper

We 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.

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