000109356 001__ 109356 000109356 005__ 20240319080946.0 000109356 0247_ $$2doi$$a10.1016/j.jfa.2021.109344 000109356 0248_ $$2sideral$$a125492 000109356 037__ $$aART-2022-125492 000109356 041__ $$aeng 000109356 100__ $$0(orcid)0000-0003-1256-3671$$aAlonso Gutiérrez, David$$uUniversidad de Zaragoza 000109356 245__ $$aBest approximation of functions by log-polynomials 000109356 260__ $$c2022 000109356 5060_ $$aAccess copy available to the general public$$fUnrestricted 000109356 5203_ $$aLasserre [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’. 000109356 536__ $$9info:eu-repo/grantAgreement/ES/MICINN PID2019-105979GB-I00$$9info:eu-repo/grantAgreement/ES/DGA/E48-20R 000109356 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/ 000109356 590__ $$a1.7$$b2022 000109356 592__ $$a1.959$$b2022 000109356 591__ $$aMATHEMATICS$$b51 / 329 = 0.155$$c2022$$dQ1$$eT1 000109356 593__ $$aAnalysis$$c2022$$dQ1 000109356 594__ $$a2.9$$b2022 000109356 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000109356 700__ $$aGonzález Merino, Bernardo 000109356 700__ $$aVilla, Rafael 000109356 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático 000109356 773__ $$g282, 5 (2022), 109344$$pJ. funct. anal.$$tJOURNAL OF FUNCTIONAL ANALYSIS$$x0022-1236 000109356 8564_ $$s727143$$uhttps://zaguan.unizar.es/record/109356/files/texto_completo.pdf$$yVersión publicada 000109356 8564_ $$s1386526$$uhttps://zaguan.unizar.es/record/109356/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000109356 909CO $$ooai:zaguan.unizar.es:109356$$particulos$$pdriver 000109356 951__ $$a2024-03-18-12:38:31 000109356 980__ $$aARTICLE