M ay 2 00 1 APPROXIMATING A NORM BY A POLYNOMIAL
نویسنده
چکیده
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 ∈ V of degree 2n such that p 1 2n (x) ≤ x ≤ n + d − 1 n 1 2n p 1 2n (x). Corollaries and polynomial approximations of the Minkowski functional of a convex body are discussed.
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تاریخ انتشار 2008