Real analytic approximations which almost preserve Lipschitz constants of functions defined on the Hilbert space

Abstract

Let $X$ be a separable real Hilbert space. We show that for every Lipschitz function $f:X\to \mathbb{R}$, and for every $\epsilon >0$, there exists a Lipschitz, real analytic function $g:X\to \mathbb{R}$ such that $|f(x)-g(x)|\le \epsilon$ and $\text{Lip}(g)\le \text{Lip}(f)+\epsilon$.

This paper has been withdrawn by the authors. The result is included in v5 of arXiv:1005.1050 (another paper by the same authors)

References in corpus (2)

• Approximation by Lipschitz, analytic maps on certain Banach spaces
• Approximation of functions and their derivatives by analytic maps on certain Banach spaces