Bernardo González Merino

activity

20132026

most citedA generalization of the discrete version of Minkowski's fundamental theorem

9 citations · 26 across the 21 of their papers we have counts for

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9 papers · 1 filter

math.FA2020

Stone-Weierstrass theorem for homogeneous polynomials and its role in convex geometry

Bernardo González Merino, Rafael Villa

We give a uniform approximation of the characteristic function of the boundary of a centrally symmetric n-dimensional compact and convex set by homogeneous polynomials of even degr…

math.FA2020

Best approximation of functions by log-polynomials

David Alonso-Gutiérrez, Bernardo González Merino, Rafael Villa

Lasserre [La] proved that for every compact set $K \subset R^{n}$ and every even number $d$ there exists a unique homogeneous polynomial $g_{0}$ of degree $d$ with $K\subset G_1(…

math.FA2019

An extension of Berwald's inequality and its relation to Zhang's inequality

David Alonso-Gutiérrez, Julio Bernués, Bernardo González Merino

In this note prove the following Berwald-type inequality, showing that for any integrable log-concave function $f : R^{n} \to [0, \infty)$ and any concave function $h:L\ri…

math.FA2019★ 1 cited

On a generalization of the Hermite-Hadamard inequality and applications in convex geometry

Bernardo González Merino

In this paper we show the following result: if C is an n-dimensional 0-symmetric convex compact set, $f : C \to [0, 1)$ is concave, and $g : [0, 1) \to [0, 1)$ is not identica…

math.FA2019

On inscribed equilateral simplices in normed spaces

Bernardo González Merino

In this paper we prove in certain n-dimensional normed spaces X the existence of full-dimensional equilateral simplices of large size inscribed to the unit ball B. This extends the…

math.FA2019

Some remarks on Petty projection of log-concave functions

Leticia Alves da Silva, Bernardo González Merino, Rafael Villa

In this note we study the Petty projection of a log-concave function, which has been recently introduced in [9]. Moreover, we present some new inequalities involving this new notio…

math.FA2018

Zhang's inequality for log-concave functions

David Alonso-Gutiérrez, Julio Bernués, Bernardo González Merino

Zhang's reverse affine isoperimetric inequality states that among all convex bodies $K \subseteq R^{n}$ , the affine invariant quantity $∣ K ∣^{n - 1} ∣ Π^{*} (K) ∣$ (where $Π^{*} (K)$ deno…

math.FA2015

John's ellipsoid and the integral ratio of a log-concave function

David Alonso-Gutiérrez, Bernardo González Merino, Carlos Hugo Jiménez +1

We extend the notion of John's ellipsoid to the setting of integrable log-concave functions. This will allow us to define the integral ratio of a log-concave function, which will e…

math.FA2014★ 1 cited

Rogers-Shephard inequality for log-concave functions

David Alonso-Gutiérrez, Bernardo González Merino, C. Hugo Jiménez +1

In this paper we prove different functional inequalities extending the classical Rogers-Shephard inequalities for convex bodies. The original inequalities provide an optimal relati…