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Nonnegative C2(R2) interpolation
Advances in Mathematics ( IF 1.7 ) Pub Date : 2020-12-01 , DOI: 10.1016/j.aim.2020.107364
Fushuai Jiang , Garving K. Luli

Abstract In this paper, we prove two improved versions of the Finiteness Principle for nonnegative C 2 ( 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 a 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.

中文翻译:

非负 C2(R2) 插值

摘要 在本文中,我们证明了非负 C 2 ( R 2 ) 插值的有限性原理的两个改进版本,之前由 Fefferman、Israel 和 Luli 证明。第一个版本将有限常数锐化到 64,第二个版本具有更好的计算实用性。在此过程中,我们还提供了一维非负 C 2 插值的详细构造,并证明不存在保持非负性的有界线性 C 2 扩展算子。
更新日期:2020-12-01
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