Optimal flat functions in Carleman-Roumieu ultraholomorphic classes in sectors
Abstract
We construct optimal flat functions in Carleman-Roumieu ultraholomorphic classes associated to general strongly nonquasianalytic weight sequences, and defined on sectors of suitably restricted opening. A general procedure is presented in order to obtain linear continuous extension operators, right inverses of the Borel map, for the case of regular weight sequences in the sense of Dyn'kin. Finally, we discuss some examples (including the well-known -Gevrey case) where such optimal flat functions can be obtained in a more explicit way.
Cite
@article{arxiv.2205.07605,
title = {Optimal flat functions in Carleman-Roumieu ultraholomorphic classes in sectors},
author = {Javier Jiménez-Garrido and Ignacio Miguel-Cantero and Javier Sanz and Gerhard Schindl},
journal= {arXiv preprint arXiv:2205.07605},
year = {2023}
}
Comments
29 pages. Important improvements, mainly in Section 3: a simplified concept of optimal flat function is introduced, and their general construction is provided for strongly non-quasianalytic weight sequences and in narrow enough sectors