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Ultraholomorphic sectorial extensions of Beurling type. (English) Zbl 1468.30057

Summary: We prove sectorial extension theorems for ultraholomorphic function classes of Beurling type defined by weight functions with a controlled loss of regularity. The proofs are based on a reduction lemma, due to the second author, which allows to extract the Beurling from the Roumieu case, which was treated recently by Jiménez-Garrido, Sanz, and the third author. To have control on the opening of the sectors, where the extensions exist, we use the (mixed) growth index and the order of quasianalyticity of weight functions. As a consequence, we obtain corresponding extension results for classes defined by weight sequences. Additionally, we give information on the existence of continuous linear extension operators.

MSC:

30D60 Quasi-analytic and other classes of functions of one complex variable
26A12 Rate of growth of functions, orders of infinity, slowly varying functions
46A13 Spaces defined by inductive or projective limits (LB, LF, etc.)
46E10 Topological linear spaces of continuous, differentiable or analytic functions
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