Ultraholomorphic sectorial extensions of Beurling type
| Autor: | Armin Rainer, Gerhard Schindl, David Nicolas Nenning |
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| Rok vydání: | 2020 |
| Předmět: |
Lemma (mathematics)
Pure mathematics Control and Optimization Algebra and Number Theory Reduction (recursion theory) Mathematics - Complex Variables 010102 general mathematics Function (mathematics) Extension (predicate logic) Type (model theory) Mathematical proof 01 natural sciences Functional Analysis (math.FA) Mathematics - Functional Analysis 010101 applied mathematics Mathematics - Classical Analysis and ODEs Classical Analysis and ODEs (math.CA) FOS: Mathematics Order (group theory) Continuous linear extension 0101 mathematics Complex Variables (math.CV) Analysis Mathematics |
| DOI: | 10.48550/arxiv.2012.12332 |
| Popis: | 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 Jim\'{e}nez-Garrido, Sanz, and the third author. In order 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. Comment: 17 pages; paper was restructured and shortened, 15 pages, accepted for publication in Annals of Functional Analysis |
| Databáze: | OpenAIRE |
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