C2interpolation with range restriction

Charles Fefferman, Fushuai Jiang, Garving K. Luli

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Given-∞< λ <Λ<∞, E ⊂Rn finite, and f:E→ [λ,Λ], how can we extend f to a Cm(Rn) function F such that λ ≤ F ≤ Λ and ||F|| Cm(Rn) is within a constant multiple of the least possible, with the constant depending only on m and n? In this paper, we provide the solution to the problem for the case m = 2. Specifically, we construct a (parameter-dependent, nonlinear) C2(Rn) extension operator that preserves the range [λ,Λ], and we provide an efficient algorithm to compute such an extension using O(N logN) operations, where N = #(E).

Original languageEnglish (US)
Pages (from-to)649-710
Number of pages62
JournalRevista Matematica Iberoamericana
Volume39
Issue number2
DOIs
StatePublished - 2023

All Science Journal Classification (ASJC) codes

  • General Mathematics

Keywords

  • Whitney problems
  • interpolation
  • non-negative
  • range restriction

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