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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.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

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

Editorial: Duke University Press

 Año de publicación: 2020

Nº de páginas: 40

Tipo de publicación: Artículo de Revista

ISSN: 1735-8787,2662-2033

Url de la publicación: https://doi.org/10.1007/s43037-020-00073-y