Best approximation of functions by log-polynomials

Alonso Gutiérrez, David (Universidad de Zaragoza) ; González Merino, Bernardo ; Villa, Rafael

Resumen: 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’.

Idioma: Inglés

DOI: 10.1016/j.jfa.2021.109344

Año: 2022

Publicado en: JOURNAL OF FUNCTIONAL ANALYSIS 282, 5 (2022), 109344
ISSN: 0022-1236

Factor impacto JCR: 1.7 (2022)

Categ. JCR: MATHEMATICS rank: 51 / 329 = 0.155 (2022) - Q1 - T1

Factor impacto CITESCORE: 2.9 - Mathematics (Q2)

Factor impacto SCIMAGO: 1.959 - Analysis (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E48-20R
Financiación: info:eu-repo/grantAgreement/ES/MICINN PID2019-105979GB-I00

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)