带范围限制的$C^2$插值

IF 1.3 2区数学 Q1 MATHEMATICS

Revista Matematica Iberoamericana Pub Date : 2021-07-17 DOI:10.4171/rmi/1353

C. Fefferman, Fushuai Jiang, Garving K. Luli

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引用次数: 3

摘要

给定−∞< λ < Λ <∞，E∧R有限，f: E→[λ，Λ]，我们如何将f扩展到C(R)函数f，使λ≤f≤Λ且‖f‖Cm(Rn)在最小可能的常数倍内，且该常数仅与m和n有关?本文给出了m = 2情况下问题的解。具体来说，我们构造了一个(参数相关的，非线性的)C(R)扩展算子，它保留了范围[λ，Λ]，并且我们提供了一个使用O(N logN)运算来计算这种扩展的有效算法，其中N = #(E)。

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$C^2$ interpolation with range restriction

Given −∞ < λ < Λ < ∞, E ⊂ R finite, and f : E → [λ,Λ], how can we extend f to a C(R) 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) C(R) 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).

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来源期刊

Revista Matematica Iberoamericana 数学-数学

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Revista Matemática Iberoamericana publishes original research articles on all areas of mathematics. Its distinguished Editorial Board selects papers according to the highest standards. Founded in 1985, Revista is a scientific journal of Real Sociedad Matemática Española.