Abstract
We prove that for any norm \(\Vert \cdot \Vert\) 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
Corollaries and polynomial approximations of the Minkowski functional of a convex body are discussed.
This research was partially supported by NSF Grant DMS 9734138.
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© 2003 Springer-Verlag Berlin/Heidelberg
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Barvinok, A. (2003). Approximating a Norm by a Polynomial. In: Milman, V.D., Schechtman, G. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1807. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36428-3_2
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DOI: https://doi.org/10.1007/978-3-540-36428-3_2
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