A Problem of Analytic Monotone Extension in Three Dimensions

Shelby Kilmer, Xingping Sun and Xiang Ming Yu
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Shelby Kilmer: Southwest Missouri State University, Department of Mathematics
Xingping Sun: Southwest Missouri State University, Department of Mathematics
Xiang Ming Yu: Southwest Missouri State University, Department of Mathematics

A chapter in Approximation, Probability, and Related Fields, 1994, pp 303-313 from Springer

Abstract: Abstract Let Ω denote the simplicial complex [0,l]d in ℝd. For a nonnegative integer p with p ≤ d, let Ω(p) denote the p-skeleton of Ω. Let d = 3 and suppose that f is a monotone function on Ω(2). We give construction schemes which extend f as a monotone function on Ω, while maintaining smoothness. Our results are related to those of Dahmen, DeVore and Micchelli for the case d = 2 and p = 1 and those of Kilmer, Sun and Yu for the case d = 3 and p = 1.

Keywords: Primary 41A05; Secondary 41A63 (search for similar items in EconPapers)
Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-2494-6_23

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DOI: 10.1007/978-1-4615-2494-6_23

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