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arXiv · 1901.09876

Nonnegative $C^2(\mathbb{R}^2)$ interpolation

Fushuai Jiang·Garving K. Luli
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Abstract

In this paper, we prove two improved versions of the Finiteness Principle for nonnegative $ C^2(\mathbb{R}^2) $ interpolation, previously proven by Fefferman, Israel, and Luli. The first version sharpens the finiteness constant to $ 64 $, and the second version carries better computational practicality. Along the way, we also provide detailed construction of nonnegative $ C^2 $ interpolants in one-dimension, and prove the nonexistence of a bounded linear $ C^2 $-extension operator that preserves nonnegativity.

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BibTeXRIS

Fushuai Jiang, Garving K. Luli. 2019-01-28. Nonnegative $C^2(\mathbb{R}^2)$ interpolation. https://arxiv.org/abs/1901.09876

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