Finiteness Principles for Smooth Selection

2015/11/16 by Charles Fefferman, Fefferman, Charles, Arie Israel +3 · 1 citation
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Mathematical Analysis and Transform Methods #math.CA #math.FA

paper · pdf · doi:10.48550/arxiv.1511.04804

106 pages

arxiv created 2015/11/27 · arxiv updated 2015/11/30

Abstract

In this paper we prove finiteness principles for C^m( ℝⁿ, ℝ^D) -selection, and for C^m-1,1( ℝⁿ, ℝ^D) -selection, in particular providing a proof for a conjecture of Brudyni-Shvartsman (1994) on Lipschitz selections for the case when the domain is X = ℝⁿ. Our results raise the hope that one can start to understand constrained interpolation problems in which e.g. the interpolating function F is required to be nonnegative everywhere.

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