Nonnegative C2(R2) interpolation

Fushuai Jiang; Garving K. Luli

doi:10.1016/j.aim.2020.107364

Nonnegative C²(R²) interpolation

Fushuai Jiang
, Garving K. Luli^*

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

6 Citations (Scopus)

Abstract

In this paper, we prove two improved versions of the Finiteness Principle for nonnegative C²(R²) 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 C² interpolants in one-dimension, and prove the nonexistence of a bounded linear C²-extension operator that preserves nonnegativity.

Original language	English
Article number	107364
Number of pages	63
Journal	Advances in Mathematics
Volume	375
Online published	17 Aug 2020
DOIs	https://doi.org/10.1016/j.aim.2020.107364
Publication status	Published - 2 Dec 2020
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2020 Elsevier Inc.

Funding

The first author is supported by the UC Davis Summer Graduate Student Researcher Award and the Alice Leung Scholarship in Mathematics. The second author is supported by NSF Grant DMS-1554733 and the UC Davis Chancellor’s Fellowship.

Research Keywords

Constrainted interpolation
Nonnegative interpolant
Nonnegative interpolation
Whitney extension problems

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Cite this

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AU - Luli, Garving K.

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AB - In this paper, we prove two improved versions of the Finiteness Principle for nonnegative C2(R2) 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 C2 interpolants in one-dimension, and prove the nonexistence of a bounded linear C2-extension operator that preserves nonnegativity. © 2020 Elsevier Inc.

KW - Constrainted interpolation

KW - Nonnegative interpolant

KW - Nonnegative interpolation

KW - Whitney extension problems

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DO - 10.1016/j.aim.2020.107364

M3 - RGC 21 - Publication in refereed journal

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VL - 375

JO - Advances in Mathematics

JF - Advances in Mathematics

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