Analytic monotone extension in two and three dimensions

Abstract

Let Ω denote the simplicial complex [0, 1]d in ℛd. For a nonnegative integer p with p ≤ d, let Ω(p) denote the p- skeleton of Ω Let d = 2 or 3 and suppose that f is a monotone function on Ω(1). 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.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1080/01630569708816751

Keywords

Analytic monotone extension, p-skeleton, Simplicial complex

Publication Date

1-1-1997

Journal Title

Numerical Functional Analysis and Optimization

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