Ultraholomorphic extension theorems in the mixed setting

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URI: https://hdl.handle.net/10902/32788
ISSN: 1735-8787
ISSN: 2662-2033
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Autoría
Jiménez Garrido, Jesús JavierAutoridad Unican; Sanz, Javier; Schindl, Gerhard
Fecha
2020-09
Derechos
© The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
Publicado en
Banach Journal of Mathematical Analysis, 2020, 14, 1630-1669
Editorial
Duke University Press
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Palabras clave
Spaces of ultraholomorphic functions
Weight sequences and weight functions
Growth indices
(non)quasianalyticity of function classes
Restriction and extension mappings
Surjectivity of the Borel map
Resumen/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.
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© The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.Excepto si se señala otra cosa, la licencia del ítem se describe como © The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.