Search results for "Logarithmically convex function"

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Analytic extension of non quasi-analytic Whitney jets of Roumieu type

1997

Let (Mr)r∈ℕ0 be a logarithmically convex sequence of positive numbers which verifies M0 = 1 as well as Mr≥ 1 for every r ∈ ℕ and defines a non quasi-analytic class. Let moreover F be a closed proper subset of ℝn. Then for every function ƒ on ℝn belonging to the non quasi-analytic (Mr)-class of Roumieu type, there is an element g of the same class which is analytic on ℝnF and such that Dα ƒ(x) = Dαg(x) for every σ ∈ ƒ0n SBAP and x ∈ F.

CombinatoricsClass (set theory)SequenceMathematics (miscellaneous)Logarithmically convex functionApplied MathematicsFunction (mathematics)Extension (predicate logic)Element (category theory)Type (model theory)MathematicsResults in Mathematics
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Analytic Extension of Non Quasi - Analytic Whitney Jets of Beurling Type

1998

Let (Mr)r∈ℕ0 be a logarithmically convex sequence of positive numbers which verifies M0 = 1 as well as Mr ≥ 1 for every r ∈ ℕ and defines a non quasi - analytic class. Let moreover F be a closed proper subset of ℝn. Then for every function f on ℝn belonging to the non quasi - analytic (Mr)-class of Beurling type, there is an element g of the same class which is analytic on ℝ,nF and such that Dαf(x) = Dαg(x) for every α ∈ ℕn0 and x ∈ F.

Discrete mathematicsClass (set theory)Pure mathematicsSequenceLogarithmically convex functionGeneral MathematicsExtension (predicate logic)Function (mathematics)Element (category theory)Type (model theory)MathematicsMathematische Nachrichten
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