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

D. Azagra; R. Fry; L. Keener

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

Functional Analysis 2015-03-23 v3

Authors: D. Azagra , R. Fry , L. Keener

Abstract

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 $\textrm{Lip}(g)\leq \textrm{Lip}(f)+\epsilon$ .

Keywords

Lipschitz functions real analytic functions Hilbert space approximation Lipschitz constant

Cite

@article{arxiv.1012.4339,
  title  = {Real analytic approximations which almost preserve Lipschitz constants of functions defined on the Hilbert space},
  author = {D. Azagra and R. Fry and L. Keener},
  journal= {arXiv preprint arXiv:1012.4339},
  year   = {2015}
}

Comments

This paper has been withdrawn by the authors.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

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

Abstract

Keywords

Cite

Comments

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