Real analytic approximations which almost preserve Lipschitz constants of functions defined on the Hilbert space
| Autor: | Azagra, D., Fry, R., Keener, L. |
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| Rok vydání: | 2010 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $\textrm{Lip}(g)\leq \textrm{Lip}(f)+\epsilon$. Comment: This paper has been withdrawn by the authors. The result is included in v5 of arXiv:1005.1050 (another paper by the same authors) |
| Databáze: | arXiv |
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