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Sectorial extensions for ultraholomorphic classes defined by weight functions
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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.
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