Finitness Principles for Smooth Selection

Charles Fefferman; Arie Israel; Garving K. Luli

Finitness Principles for Smooth Selection

Functional Analysis 2016-03-09 v1 Classical Analysis and ODEs

Authors: Charles Fefferman , Arie Israel , Garving K. Luli

Abstract

In this paper we prove finiteness principles for $C^{m}\left( \mathbb{R}^{n}, \mathbb{R}^{D}\right)$ -selection, and for $C^{m-1,1}\left( \mathbb{R}^{n}, \mathbb{R}^{D}\right)$ -selection, in particular providing a proof for a conjecture of Brudyni-Shvartsman (1994) on Lipschitz selections for the case when the domain is $X = \mathbb{R}^n$ .

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@article{arxiv.1603.02323,
  title  = {Finitness Principles for Smooth Selection},
  author = {Charles Fefferman and Arie Israel and Garving K. Luli},
  journal= {arXiv preprint arXiv:1603.02323},
  year   = {2016}
}

Comments

This is the first part of the paper titled "Finiteness Principles for Smooth Selection" arXiv:1511.04804 . A new corollary (Corollary 4 in Section III.1) has been added. The original paper is split into two parts for publication convenience

Finitness Principles for Smooth Selection

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