C2 interpolation with range restriction

被引：3

作者：

Fefferman, Charles ^{[1
]}

Jiang, Fushuai ^{[2
]}

Luli, Garving K. ^{[2
]}

机构：

[1] Princeton Univ, Dept Math, Fine Hall,304 Washington Rd, Princeton, NJ 08544 USA

[2] Univ Calif Davis, Dept Math, Math Sci Bldg,1 Shields Ave, Davis, CA 95817 USA

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2023年 / 39卷 / 02期

基金：

美国国家科学基金会;

关键词：

Whitney problems; interpolation; range restriction; non-negative; M-SMOOTH FUNCTION; WHITNEYS EXTENSION PROBLEM; SET-VALUED MAPPINGS; C-M EXTENSION; LIPSCHITZ SELECTIONS; FINITENESS PRINCIPLES; CLOSED SUBSET; SPLINES; POINT; SPACE;

D O I：

10.4171/RMI/1353

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given-8 < ? < ? < 8, E C R-n finite, and f : E -[?, ?], how can we extend f to a C-m(R-n) function F such that ? = F=A and IIF IIC m(R-n) 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. Specifi-cally, we construct a (parameter-dependent, nonlinear) C-2(R-n) extension operator that preserves the range [A, A], and we provide an efficient algorithm to compute such an extension using O(N log N) operations, where N = #(E).

引用

页码：649 / 710

页数：62

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