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Sectorial extensions for ultraholomorphic classes defined by weight functions
Author(s) -
JiménezGarrido J.,
Sanz J.,
Schindl Gerhard
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800465
Subject(s) - mathematics , extension (predicate logic) , mathematical proof , weight function , transfer (computing) , pure mathematics , sequence (biology) , function (biology) , reduction (mathematics) , algebra over a field , discrete mathematics , calculus (dental) , mathematical analysis , geometry , medicine , dentistry , evolutionary biology , parallel computing , biology , computer science , genetics , programming language
We prove an extension theorem for ultraholomorphic classes defined by so‐called Braun–Meise–Taylor weight functions ω and transfer the proofs from the single weight sequence case from V. Thilliez to the weight function setting. We are following a different approach than the results obtained in a recent paper by the authors, 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.