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Continuous Linear Extension of Ultradifferentiable Functions of Beurling Type

✍ Scribed by Uwe Franken

Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
965 KB
Volume
164
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

For a weight function Ο‰ and a closed set A βŠ‚ ℝ^N^ let β„°~(Ο‰)~(A) denote the space of all ω‐Whitney jets of Beurling type on A. It is shown that for each closed set A βŠ‚ ℝ^N^ there exists an ω‐extension operator EA: β„°~(Ο‰)~(A) β†’ β„°~(Ο‰)~(ℝ^N^) if and only if Ο‰ is a (DN)‐function (see MEISE and TAYLOR [18], 3.3). Moreover for a fixed compact set K βŠ‚ ℝ^N^ there exists an ω‐extension operator E~K~: β„°~(Ο‰)~(K) β†’ β„°~(Ο‰)~(ℝ^N^) if and only if the FrΓ©chet space β„°~(Ο‰)~(K) satisfies the property (DN) (see Vogt [29], 1.1.).

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