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• W3042953477 abstract "Lasserre [La] proved that for every compact set $Ksubsetmathbb R^n$ and every even number $d$ there exists a unique homogeneous polynomial $g_0$ of degree $d$ with $Ksubset G_1(g_0)={xinmathbb R^n:g_0(x)leq 1}$ minimizing $|G_1(g)|$ among all such polynomials $g$ fulfilling the condition $Ksubset G_1(g)$. This result extends the notion of the Lowner ellipsoid, not only from convex bodies to arbitrary compact sets (which was immediate if $d=2$ by taking convex hulls), but also from ellipsoids to level sets of homogeneous polynomial of an arbitrary even degree. In this paper we extend this result for the class of non-negative log-concave functions in two different ways. One of them is the straightforward extension of the known results, and the other one is a suitable extension with uniqueness of the solution in the corresponding problem and a characterization in terms of some 'contact points'." @default.
• W3042953477 created "2020-07-23" @default.
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• W3042953477 date "2020-07-15" @default.
• W3042953477 modified "2023-09-27" @default.
• W3042953477 title "Best approximation of functions by log-polynomials" @default.
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