Mixed ultraholomorphic extension theorems hold for sector openings controlled by new mixed growth indices γ(M,N) and γ(σ,ω), even when all unmixed indices vanish.
Sectorial extensions for ultraholomorphic classes defined by weight functions
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abstract
We prove an extension theorem for ultraholomorphic classes defined by so-called Braun-Meise-Taylor weight functions and transfer the proofs from the single weight sequence case from V. Thilliez [28] to the weight function setting. We are following a different approach than the results obtained in [11], more precisely we are working with real methods by applying the ultradifferentiable Whitney-extension theorem. We are treating both the Roumieu and the Beurling case, the latter one is obtained by a reduction from the Roumieu case.
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Ultraholomorphic extension theorems in the mixed setting
Mixed ultraholomorphic extension theorems hold for sector openings controlled by new mixed growth indices γ(M,N) and γ(σ,ω), even when all unmixed indices vanish.