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- W1973190045 abstract "Let $X$ be a separable Banach space with a separating polynomial. We show that there exists $Cgeq 1$ (depending only on $X$) such that for every Lipschitz function $f:Xrightarrowmathbb{R}$, and every $epsilon>0$, there exists a Lipschitz, real analytic function $g:Xrightarrowmathbb{R}$ such that $|f(x)-g(x)|leq epsilon$ and $textrm{Lip}(g)leq Ctextrm{Lip}(f)$. This result is new even in the case when $X$ is a Hilbert space. Furthermore, in the Hilbertian case we also show that $C$ can be assumed to be any number greater than 1." @default.
- W1973190045 created "2016-06-24" @default.
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- W1973190045 date "2010-05-06" @default.
- W1973190045 modified "2023-10-14" @default.
- W1973190045 title "Real analytic approximation of Lipschitz functions on Hilbert space and other Banach spaces" @default.
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- W1973190045 doi "https://doi.org/10.48550/arxiv.1005.1050" @default.
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