[Banach] Abstract of a paper by Daniel Azagra and Carlos Mudarra

This is an announcement for the paper “An Extension Theorem for convex functions of class $C^{1,1}$ on Hilbert spaces” by Daniel Azagra and Carlos Mudarra.

Abstract: Let $H$ be a Hilbert space, $E\subset H$ be an arbitrary subset and $f : E\rightarrow R, G: E\rightarrow H$ be two functions. We give a necessary and sufficient condition on the pair $(f, G)$ for the existence of a convex function $F\in C^{1,1}(H)$ such that $F=f$ and $\nabla F= G$ on $E$. We also show that, if this condition is met, $F$ can be taken so that Lip$(\nabla F)=$Lip$(G)$.

The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.00241