109356 20240319080946.0 doi 10.1016/j.jfa.2021.109344 sideral 125492 ART-2022-125492 eng Alonso Gutiérrez, David Universidad de Zaragoza (orcid)0000-0003-1256-3671 Best approximation of functions by log-polynomials 2022 Access copy available to the general public Unrestricted Lasserre [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’. info:eu-repo/grantAgreement/ES/DGA/E48-20R info:eu-repo/grantAgreement/ES/MICINN PID2019-105979GB-I00 info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 1.7 2022 MATHEMATICS 51 / 329 = 0.155 2022 Q1 T1 1.959 2022 Analysis 2022 Q1 2.9 2022 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion González Merino, Bernardo Villa, Rafael 2006 015 Universidad de Zaragoza Dpto. Matemáticas Área Análisis Matemático 282, 5 (2022), 109344 J. funct. anal. JOURNAL OF FUNCTIONAL ANALYSIS 0022-1236 727143 http://zaguan.unizar.es/record/109356/files/texto_completo.pdf Versión publicada 1386526 http://zaguan.unizar.es/record/109356/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:109356 articulos driver 2024-03-18-12:38:31 ARTICLE