doi:10.1016/j.jfa.2021.109344engAlonso Gutiérrez, DavidGonzález Merino, BernardoVilla, RafaelBest approximation of functions by log-polynomialsART-2022-125492Lasserre [La] proved that for every compact set K _ Rn and every even number d there exists a unique homogeneous polynomial g0 of degree d with K _ G1(g0) = fx 2 Rn : g0(x) _ 1g minimizing jG1(g)j among all such polynomials g fulfilling the condition K _ G1(g). This result extends the notion of the Löwner 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’.2022http://zaguan.unizar.es/record/10935610.1016/j.jfa.2021.109344http://zaguan.unizar.es/record/109356oai:zaguan.unizar.es:109356info:eu-repo/grantAgreement/ES/DGA/E48-20Rinfo:eu-repo/grantAgreement/ES/MICINN PID2019-105979GB-I00JOURNAL OF FUNCTIONAL ANALYSIS 282, 5 (2022), 109344by-nc-ndhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccess