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Ultraholomorphic extension theorems in the mixed setting

Abstract: The aim of this work is to generalize the ultraholomorphic extension theorems from V. Thilliez in the weight sequence setting and from the authors in the weight function setting (of Roumieu type) to a mixed framework. Such mixed results have already been known for ultradifferentiable classes and it seems natural that they have ultraholomorphic counterparts. In order to have control on the opening of the sectors in the Riemann surface of the logarithm for which the extension theorems are valid we are introducing new mixed growth indices which are generalizing the known ones for weight sequences and functions. As it turns out, for the validity of mixed extension results the so-called order of quasianalyticity (introduced by the second author for weight sequences) is becoming important.

Other publications of the same journal or congress with authors from the University of Cantabria

 Fuente: Banach Journal of Mathematical Analysis, 2020, 14, 1630-1669

 Publisher: Duke University Press

 Publication date: 01/09/2020

 No. of pages: 40

 Publication type: Article

 DOI: 10.1007/s43037-020-00073-y

 ISSN: 1735-8787,2662-2033

 Spanish project: MTM2016-77642-C2-1-P

 Publication Url: https://doi.org/10.1007/s43037-020-00073-y

Authorship

SCHINDL, GERHARD