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

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

2010-12-20

arxiv.org/abs/1012.4339v2

Mathematics

Functional Analysis

Some misprints corrected

Scientific paper

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

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