Summary
Let ω be a weight in the sense of Braun, Meise, Taylor, which defines a non-quasianalytic class. Let H be a compact subset of ℝn. It is proved that for every function ƒ on ℝn which belongs to the non-quasianalytic (ω)-class, there is an element g of the same class which is analytic on ℝn\H and such that Dα ƒ(x) = Dα g(x) for every x ∈ H and α ∈ ℕ n0 . A similar result is proved for functions of the Roumieu type. Continuous linear extension operators of Whitney jets with additional properties are also obtained.
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Supported in part by DGICYT PB91-0326
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Valdivia, M. On certain linear operators in spaces of ultradifferentiable functions. Results. Math. 30, 321–345 (1996). https://doi.org/10.1007/BF03322199
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DOI: https://doi.org/10.1007/BF03322199