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Article overview
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Finiteness Principles for Smooth Selection | Charles Fefferman
; Arie Israel
; Garving K. Luli
; | Date: |
16 Nov 2015 | Abstract: | In this paper we prove finiteness principles for $C^{m}left( mathbb{R}^{n},
mathbb{R}^{D}
ight) $-selection, and for $C^{m-1,1}left( mathbb{R}^{n},
mathbb{R}^{D}
ight) $-selection, in particular providing a proof for a
conjecture of Brudyni-Shvartsman (1994) on Lipschitz selections for the case
when the domain is $X = mathbb{R}^n$. 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. | Source: | arXiv, 1511.4804 | Services: | Forum | Review | PDF | Favorites |
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