Carlos Mudarra

activity

20162026

collaborators

Showing math.FAShow all

7 papers · 1 filter

math.FA2019

Convex $C^{1}$ extensions of $1$ -jets from compact subsets of Hilbert spaces

Daniel Azagra, Carlos Mudarra

Let $X$ denote a Hilbert space. Given a compact subset $K$ of $X$ and two continuous functions $f : K \to R$ , $G : K \to X$ , we show that a necessary and sufficient condition for…

math.FA2019

Prescribing tangent hyperplanes to $C^{1, 1}$ and $C^{1, ω}$ convex hypersurfaces in Hilbert and superreflexive Banach spaces

Daniel Azagra, Carlos Mudarra

Let $X$ denote $R^{n}$ or, more generally, a Hilbert space. Given an arbitrary subset $C$ of $X$ and a collection $H$ of affine hyperplanes of $X$ such that every…

math.FA2018

Extensions of convex functions with prescribed subdifferentials

Daniel Azagra, Juan Ferrera, Javier Gómez-Gil +1

Let $E$ be an arbitrary subset of a Banach space $X$ , $f : E \to R$ be a function, and $G : E ⇉ X^{*}$ be a set-valued mapping. We give necessary and su…

math.FA2018

Kirszbraun's theorem via an explicit formula

Daniel Azagra, Erwan Le Gruyer, Carlos Mudarra

Let $X, Y$ be two Hilbert spaces, $E$ a subset of $X$ and $G : E \to Y$ a Lipschitz mapping. A famous theorem of Kirszbraun's states that there exists $G : X \to Y$ with…

math.FA2018

Approximation of Lipschitz functions preserving boundary values

Robert Deville, Carlos Mudarra

Given an open subset $Ω$ of a Banach space and a Lipschitz function $u_{0} : Ω \to R,$ we study whether it is possible to approximate $u_{0}$ uniformly on $Ω$ by $C^{k}$ …

math.FA2017

Explicit formulas for $C^{1, 1}$ and $C_{conv}^{1, ω}$ extensions of $1$ -jets in Hilbert and superreflexive spaces

Daniel Azagra, Erwan Le Gruyer, Carlos Mudarra

Given $X$ a Hilbert space, $ω$ a modulus of continuity, $E$ an arbitrary subset of $X$ , and functions $f : E \to R$ , $G : E \to X$ , we provide necessary and sufficient conditions…

Convex C1 extensions of 1-jets from compact subsets of Hilbert spaces

Prescribing tangent hyperplanes to C1,1 and C1,ω convex hypersurfaces in Hilbert and superreflexive Banach spaces

Extensions of convex functions with prescribed subdifferentials

Kirszbraun's theorem via an explicit formula

Approximation of Lipschitz functions preserving boundary values

Explicit formulas for C1,1 and Cconv1,ω​ extensions of 1-jets in Hilbert and superreflexive spaces

Convex $C^{1}$ extensions of $1$ -jets from compact subsets of Hilbert spaces

Prescribing tangent hyperplanes to $C^{1, 1}$ and $C^{1, ω}$ convex hypersurfaces in Hilbert and superreflexive Banach spaces

Explicit formulas for $C^{1, 1}$ and $C_{conv}^{1, ω}$ extensions of $1$ -jets in Hilbert and superreflexive spaces