Approximation and Extension of C∞ Functions Defined on Compact Subsets of ℂn

Wiesław Pawłucki and Wiesław Pleśniak
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Wiesław Pawłucki: Jagiellonian University, Institute of Mathematics
Wiesław Pleśniak: Jagiellonian University, Institute of Mathematics

A chapter in Deformations of Mathematical Structures, 1989, pp 283-295 from Springer

Abstract: Abstract A topological linear embedding into the Fréchet space of rapidly decreasing sequences is constructed (Section 6) on a (fat) compact subset of ℝn whose Siciak’s extremal function is Ho̎lder continuous. The existence of such an embedding appears to be equivalent to the existence of a continuous linear extension for C∞ functions. Thus, the main result of our previous paper [8] is reproved in a different way. Also a ‘complex’ version of Bernstein’s theorem, proved earlier in our paper [7], is given.

Keywords: Compact Subset; Extension Operator; Extremal Function; Lagrange Interpolation; Continuous Linear Operator (search for similar items in EconPapers)
Date: 1989
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DOI: 10.1007/978-94-009-2643-1_26

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