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Extension operators for real analytic functions on compact subvarieties of

✍ Scribed by Vogt, Dietmar

Book ID
118740379
Publisher
Walter de Gruyter GmbH & Co. KG
Year
2007
Tongue
English
Weight
181 KB
Volume
2007
Category
Article
ISSN
0075-4102

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Extension operators for real analytic fu
Extension operators for real analytic functions on compact subvarieties of
✍ Vogt, Dietmar πŸ“‚ Article πŸ“… 2007 πŸ› Walter de Gruyter GmbH & Co. KG 🌐 English βš– 181 KB

Let X be a compact coherent real analytic subvariety of R d . It is shown that a continuous linear operator which extends real analytic functions on X to real analytic functions on R d exists if and only if X is of type PL, which means that in every point of X the local complexification satisfies Ho

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## Abstract It is shown that for an algebraic subvariety __X__ of ℝ^__d__^ every FrΓ©chet valued real analytic function on __X__ can be extended to a real analytic function on ℝ^__d__^ if and only if __X__ is of type (PL), i.e. all of its singularities are of a certain type. Necessity of this cond

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Let Ω1, Ω2 be open subsets of R d 1 and R d 2 , respectively, and let A(Ω1) denote the space of real analytic functions on Ω1. We prove a Glaeser type theorem by characterizing when a composition operator CΟ• : Using this result we characterize when A(Ω1) can be embedded topologically into A(Ω2) as